You want to be very careful testing a thing like this especially with test gear that is only "good" for 600 or 1000V.
Neon signs use a secondary side voltage (depending upon the size of the sign) of between 15 and 50kV.
The wires on these signs need to have the proper silicone insulated wires, you can't use ordinary wire at these voltages, especially if they are exposed to the weather.
I went to a place a few years back where people were getting shocks (not just a tingle) off the doors in a restaurant kitchen, I found that the neon sign on the roof had really dodgy wiring and was leaking to earth via the steel roof and framework, but not enough current to blow any protection gear.
My advice would be to tell the guy to get a proper sign guy to have a look at the install, it sounds like it needs some work.