Concerts demand songs. People who are sitting and listening, instead of dancing, want to be drawn in, and singing does this in a way that pure instrumental pieces don't. I don't know whether you can hum the first movement of Beethoven's 9th Symphony, but I'll bet you can hum the last.
Bluegrassers understand this. People will toss more money in your case if you're busking on the mall or in the subway when you sing than when you play straight fiddle tunes. Lifting material from The New Lost City Ramblers or Uncle Dave Macon or Charlie Poole will get you better coffee after a day's playing in the hot sun.
Radio gigs, too. If you go on the radio, most folks listening to you in the car will use your instrumentals as a time to surf the dial for a more interesting station. What instrumental tunes can you list that have made the rock charts? "Walk, Don't Run," by the Ventures? Sure. Mason Williams' "Classical Gas"? Okay. Little Stevie Wonder's "Fingertips (Part 2)"? Mostly instrumental because you can't sing much when your instrument's a harmonica. And, uh, uh, uh ... Hey, I'm thinking. It'll come to me.
Jams and festivals, for sure. Fergus Stone's singing raises the quality of every fiddle jam he graces.
If you play weddings and other parties, the guests will say nicer things about the band if you sing to them. When the bride's drunk uncle calls for The Ballad of Jed Clampett, having a basket of singing tunes lets you say, "We don't know that one, but here's one like it."
But dances? That's trickier.
At a contra, you can often slip in a verse or a chorus once the caller's mostly stopped calling. This means that if you have something you could possibly sing, make it the last tune in your set. Even then, watch carefully, a time or two through, to convince yourself that you're not going to step on anything. If the caller is still prompting them at the start of A1 and B1, sing on A2 or B2. Most callers want to call the whole dance the last time through, so don't wait until the very end. Don't call if the dance is marginal, because the caller may need to start calling again to straighten things out.
The break in the middle can be a good time to do a song, too. We often do a swing tune or two, and we can make those vocals, because they're not called. Don't take up the whole break, though, because folks want to chat, and you shouldn't make them have to talk over you. If there's a separate place they can go to talk besides the dance floor, you have more options.
You can do a song after the dance ends, too, to cap the evening, if you arrange this beforehand, especially with whoever's doing and packing up the sound. It's embarrassing when your amp shuts down in the middle of a song, and the speakers and mikes go dead.
Arrange for a vocal mike, and adjust it as part of the sound check. Set the monitors by singing into it with the full band. Have it on for the songs, and off otherwise. Unless there's a switch on the mike, this is in the hands of whoever's running the boards, so if you're ready to kick into a song but the guy running sound is off in the kitchen, you are out of luck.
At some point, I realized that waltzes aren't called, either, and we could try singing waltzes. Dancers ran up to the stage afterwards to thank us. At next week's dance, where I wasn't playing, I had dancers complimenting me as I danced with them. "I really loved it when you did 'The Tennessee Waltz.' "
We worked up a repertoire of singing waltzes.
One of the local dances stopped booking us. Someone from that community confessed, in private, that it was because the guy who was booking their bands didn't approve of singing waltzes.
Damned if you do, damned if you don't.