Sometimes, when I am trying to make contacts, I call out on a bunch of repeaters due to low activity on individual repeaters. I usually call out, wait 10 seconds, then change repeater. Is there a specific length I should wait to see if anyone is on the repeater before changing frequency and trying out another repeater?
This would depend on local practice.
Generally speaking, I'd wait at least for the repeater's sign-off notification (or carrier drop-out if it has a long output carrier hold), then preferably a little longer before moving on to another repeater or frequency.
Not everyone can drop what they are doing and grab the microphone right away, so ten seconds is pretty short. Now, imagine that they also have their radio set to scan a handful of repeaters or they have more than one radio, and might have to stop the scan or see which radio the transmission was received on. Even an experienced operator might need a second or two just for that.
Of course, if when you do get a response you normally get it within 2-3 seconds, then waiting for 10 seconds may be plenty. But I for one wouldn't count on it.