This is a separate battery that powers the lift. The V10 in the truck has it's own battery. There's a switch in the cab to activate power to the lift. The way it's been explained to me, when that switch is on, the lift battery powers the lift and is isolated from the rest of the charging system so that the truck battery doesn't get sapped. When the lift switch is off, the truck alternator charges that battery.
I'm kind of leaning toward the NAPA deep cycle (I believe Deka makes their batteries) in my earlier link, but the listing doesn't show amp hours.
I'd definitely go deep-cycle for your application. Deka or Trojan.
Your battery isolator switch does it's job - guaranteeing you can start the truck. Public Utility crews often just leave the truck running, so don't have the issue you describe. Then again, they don't pay for their own fuel - guessing that you do.
Even a deep cycle battery does not like to be deeply discharged, often - they survive this use better than starting batteries, but that is somewhat a damning with faint praise comparison. At the end of the day/week, battery maintainers can help, but your in-day use can be a factor too.
If you work 30 minutes at one site, then drive 40+ miles to another job, a healthy alternator should keep a hyd. pack battery happily topped up - given that the isolator switch is returned to the Charge position.
OTOH, if you work at one site for 2 hours, drive 1 mile to another site, work 3 hours..... you get the picture.... your hyd. pack battery may be suffering at the end of a long day like that.
Depending on your truck use patterns, I'd be tempted to hook up something like a Honda EU2000i to the hyd. pack battery - quiet, and they can put out 8amps DC for battery charging. Fire it up when you are parked on site - no matter how long you are there, the hyd. battery should be fine. A small Honda can be a good solution, but any generator+battery charger would work for this though. Some Telco trucks run on-board generators, for similar reasons.
(P.S. I'm no expert on bucket trucks, I'm only guessing at 8 amps being enough - I'm assuming just sporadic bucket movement for positioning, and light hyd. tool use now and then.).
Rgds, D.