Answer:

“And when men and women who profess to be Christians and never testify to the unsaved, or let their light shine, there's something wrong with that individual. God wants you to let the light shine; give Him praise anywhere, as Paul said of old, "I'm not ashamed of the Gospel, for it's the power of God unto salvation.” [Hear Ye Him, Edmonton Alberta, 57-0807]
“Joel said, "I'll pour out My Spirit upon all flesh, and your sons and your daughters shall prophesy." Now, the word "prophesy" does not mean to teach.
The "prophesy" means to either "tell an experience under inspiration," or "foretell something that's fixing to take place." And we know that there was prophetess in the Old Testament. They never could speak out in the building, speak out in the church, in the congregation, as a teacher. But, see, Anna and many of them in the temple, they were prophetesses, and Miriam was a prophetess or something like that. She had the Spirit on her; that's true; but she had her limitations of place.
Women can be prophetess today, absolutely; but not teachers, and so forth, behind the platform here. If you do, you make--you make the Bible contradict itself.” [Why Are We Not A Denomination, Jeff In 58-0927]

“May these women go home to their husbands and to their children, this little boy to his papa and mama, a new creature, a new person, going home to live, to testify in the neighborhood, to be instruments to bring others to You. For we realize that we're at the end time and You're making Your last call across the nation.” [To Whom Would We Go, Chautauqua, Oh, 60-0606]

“Now, someone had give me a note here, just a little question. We won't take too much time now to answer it. And remember, each time you lay a little question up, I'll try my best to get to it if I can. But this was an important question. One wanted to know if it was wrong for women to testify, or to sing, or give messages in tongue, interpretate the messages, or prophecy in the church. No, it isn't wrong; it's a--as long as it comes in the place in order. See?

But women are gifted with prophecy, and gifted with tongues and interpretations, and everything but being preachers. They're not to be preachers. They're forbidden to preach in the churches (That's right.), take the place, or be a teacher, or anything in the church. But as far as gifts, the woman has all those, can occupy one or any of those nine spiritual gifts according to I Corinthians 12, and is under no bondage that her message should not come forth in its place.” [The Patmos Vision, Jeff.In60-1204e]

“Women, housewife, no matter if you're the maid in somebody's house, testify. Do everything you can for the Kingdom; but don't ever inject your own ideas; just say what the Message says and keep going on. (See?) And then maybe you'd have some influence. Well, don't try to preach now until God, you know calls you. Just stay right with that, your testimony, because if you don't, you'll get off in the wrong category; and then you'll mess up everything. That's it. And it doesn't please God at all. This proves it here.” [The Influence Of Another, Jeff In, 62-1013]

“There was a little mother walking around packing a little baby; and there was another little mother setting there, typical little Southern mother with a little gingham or calico, or ever what you call it, dress on. And she said, just a little housewife, but the Lord kept dealing with that woman, "Go, pray for that baby." Why, she looked and the woman had a prayer card. "Oh," she said, "I, I'd be afraid to go pray for that baby, Brother Branham's going to pray for that baby tonight." Said, "The woman's got a prayer card." And said, "He... Why, I wouldn't do it." And he turned... She turned around; the Lord said to her, just revealed to her heart, "Go, pray for that baby."
Well, it just kept haunting her so much; she said, "Well, if the woman comes back through here again, I'm going to stop her." So she said, "Lady, would you take my seat and set down here; I know you're just wore out with that baby, and he won't be here for a couple of hours yet?" Said, "Thank you, sister," said, "I appreciate... I hate to take your seat." Said being then we got into conversation, "Would you mind if I just offer a little word of prayer for the baby? I see you got a prayer card. Perhaps, Brother Branham will pray for the baby tonight." Said, "But just to relieve my feeling, would you mind if I offer a little prayer?" She said, "Why, certainly not, sister, dear." And she held the little baby out, and the little mother laid her hands over on the baby and prayed a simple little prayer.
And then the little woman couldn't have no place to set down, so she went way up in the balcony in the gymnasium. And so she got up there, and about a couple hours later when I come in, prayer cards was called and the little woman was standing in the line. So the little woman up in the balcony, she said, "Oh, my. Maybe I shouldn't have done that, but I felt better after I done it." When the little woman come up in the line with the baby, the Holy Spirit come, begin to talk to the woman, tell her who she was and what was the matter with her baby, but said, "You know, your baby is already healed, 'cause a little lady has prayed for her, with a little calico dress on, is standing right up there in the balcony. God's already heard her prayer, and the baby is already healed. You don't have to worry about it; it's all right." Now, what if the little mother had failed to do what God told her to do? See? Now, see, it wasn't the evangelist's place. God works in all the laity. He... We have certain jobs to do, but you have to pray one for another. That... And God will take care of you.” [God's Covenant With Abraham, Charlotte, NC 56-0428]

“And if each one of you in here now has not been positionally placed... You might not be nothing but a housewife. Well, you say, "Brother Branham, I never done a thing in my life. I'm not a preacher." Well, maybe God brought you here to raise a family of children; out of that family of children may come another family of children, that'll be a preacher that'll send a million souls to Christ. You had to be here. You're here for a purpose. Did you know that?” [Adoption Pt4 , Jeff, IN, 60-0522e]

“If you're a good lay member, be a good lay member. If--if you're a good housewife, and God's blessed you as a housewife and made you loyal and true, sister, you just continue to be that. Don't get thinking you're--God called you to be a preacher, or--or a deacon, or something else. And you do the same, men. Wherever God has blessed you, there abide, 'cause that's where He's set you at. You do just what He tells you to do, and see where He blesses you. But don't ever try to step in.” [Influence, Beaumont, TX, 64-0315]

(We truly appreciate the help of Brother Donny Reagan in researching answers to the question above)