Is there at least one booth that is manned 24/7 for cash payments? Which sign to drive to?
For what country? I'm assuming Italy. If so, look at the sign that shows a person holding out their hand and make sure that lane has a green indicator meaning it is open. Otherwise, enter the lane that shows "bills and coins" for Euros only.
I found staffed booths by following the sign of a human hand handling cash, as in the photo at http://www.accessitaly.com/post/Driving-in-Italy-part-5-e28094-Paying-Autostrade-Tolls.aspx. I doubt that you really want to be driving late at night, but in that case, do make clear arrangements with your hotel.
The sign for cash payment is WHITE and displays a CASH logo (bills and coins).
If it's manned it will show a BLACK HAND holding the cash, otherwise it's a self service machine where you insert the cash for payment (it gives back change).
Some minor exits are 100% automated, meaning that there are no manned booths. As I mentioned the self service cash payment machine is easy to use and gives back change, so you don't need to have the exact toll amount.
You can also pay by credit card at the automated booths, but I believe you can do so ONLY with CHIP & PIN cards (don't know for sure because I always use cash).
Take a look at the pictures of the booth signs below:
https://www.autostrade.it/it/il-pedaggio/pagamento-al-casello
A few exits have only machines, some of them accepting cash as well as credit cards, but most exits have at least a booth continuously manned.
I remember some that were totally automated or times when the manned booths were not in service but those were usually at smaller towns. Bigger towns and cities should usually have a manned booth (but it is Italy so don't always count on what should be). It's been three years since I left and suppose it could've changed but never had a problem with my mag stripe credit card at toll booths, only gas pumps.