Probably had it on to listen and grabbed it, squeezing the mic switch in the process.
Any hams know if or how they can ID a hand-held by it having broken squelch?
There is also "tranmitter fingerprinting" but it requires a long set up and more equipment than you will find in the field.
It depends on the system. LASO's move to 480 mhz is fairly recent, so they most likely have the identifiers built in. They're a little digital tone generator that sends a serial number identifying the radio number any time you key the mike. The dispatch system maintains a database cross-referencing radio serial number and unit number on an ongoing basis.
With respect to the question about the absence of identifying information on the audio feed we're getting, the system is a type known as "repeater duplex", with the cars on one frequency and the dispatcher on another. The car radios are picked up and rebroadcast on the base frequency, and in the process the little "identifier squawk" is cut out. If we were listening directly to the units, I suspect we'd be hearing it.
Even though it's called a TAC frequency, it's repeater duplex, thus the confusion among the troops. LAPD's system allows "direct" communication without triggering the repeater, and in that mode you can hear the "squawk". LASO probably has something similar. and they may be using it along with cell phones in addition to the more publicly accessable communications.
If he has the deputy's radio, it probably has the local TAC frequencies programmed in, but it was most likely tuned to the Antellope Valley base frequency. So, I guess we can look at the guy's picture and try to figure out whether's he's bright enough to switch frequencies.