Update on my situation which might be helpful to OP's concern:

My battery was borked. The seal connecting the terminal to the cables was corroded to the point where it was corroding the battery itself, and the whole thing definitely needed to be replaced.

The cart guy checked the switch beneath the gas pedal, it was fine, no problems with it. Whatever thing that houses the governor needed a little tweak, because it was going slower than it was allowed to go, and this happened abruptly last year when it USED to go faster than it was allowed to go and just - stopped doing that - for no apparent reason. So now it's going as fast as it's allowed to go, which is fine by me.

Meanwhile, he said the starter generator is fairly worn out, which is the cause (in my situation) of the occasional hesitancy between depressing the gas pedal and acceleration. He says it could stay that way indefinitely, or I could have it replaced for $480. It could also some day fail, but he didn't seem too concerned about the possibility of that happening any time soon. So I'll just live with occasional hesitancy and be over-cautious at stop signs with a crossroad that doesn't have a stop sign.

You do not mention the make/model of the cart, but some of the generator/starter have replaceable brushes, much lower cost than replacing the whole unit. Check with some other golf cart repair services that come to your house, you may be very surprised.

Also, back to the original thread, a friend just had exactly the same hesitation problem. I checked the ignition switch, the starter, and the solenoid and the battery. The battery showed a slightly low (2 volts) below normal, but did not come up the normal with the cart running. He took cart to store where purchased, they determined it was a bad cell in the battery, replaced under warranty.

How old is the battery ? Check that first.