They may not be burning out. Pop bumper bulbs take a beating. How long are they lasting? Just one pop bumper?

Bally bumper lamps run at about 6.3v AC or DC depending on weather they are GI, (on all the time) or DC (when lit by the computer). Either way Bally bumper lamps are notorious for early failure. It's due to the vibrations of the game. Not much you can do about it.
Switching to LEDs might minimize the problem.

I've got three machines, 2 EM and 1 early SS and replaced all pop bumper sockets during refurb and installed 'warm white' LED replacement lamps...haven't had a lick of trouble. You get brighter light and they won't brown those precious pop covers.

Great advice but working on pop bumpers may be pretty intimidating for someone who has little experience working on their pins. Maybe start with just replacing the bulb with an led first and see if it helps.

There's lots of Utube channels discussing how to read schematics, even specifically pinball schematics. Same with using a multimeter. If not sure of the voltage based on looking at the schematics, take a reading with AC and DC. Chances are only one will have a "real" reading, and the other will be very low or not repeatable.

The Mystic schematics on IPDB are a little hard to read because the are paginated and the second half is smaller than the first so you can’t match them up. So the GI is shown here to be connected to A2J2 pins 1 and 5. A2 is the rectifier board which is attached to the transformer. If you look at schematic for the transformer you will see that pins 1 and 5 come directly off the transformer winding for 7.3 vac (after going through a fuse) which you can measure at Test Point 3 on the rectifier board. Therefore GI voltage is ac. The other windings go to full wave rectifiers and get changed to dc voltage so anything connected to those points you would measure dc voltage. Hope this helps a little. Learning to read schematics takes some time. The best way is to look at the drawings and when you think you know what it says, go to the game and verify your theory. Back and forth a few times and you will become more confident.

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I like incandescent but relented to put LED's under the pops

I wonder if because the #47's have a lighter filiment than the #44's it makes em susceptible to burning out quicker due to vibration.

To help solve some of the mystery of where a particular wire may go (in this case the general illumination) I color coded the "A2J2-1 & A2J2-5) in a couple places .... hope it helps
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Cute pooch...otherhoo, doncha kno eh, all yah need is a few wrenches, a couple of screwdrivers, a soldering iron, proper replacement parts, and thorough analysis of the parts breakdown...a pic or two prior to diving in and disassembling, a UTube vid or two...and REBUILT! I'm a native Yooper, by the way, hence the early language -- -- DIVE IN, otherwise you're forever scared!