I've got 2 of them. Both use 12V 23A batteries (same unit purchased yrs apart that came in different style cases) & both of mine came with batteries. They use only one. 23A batteries were commonly used in older automotive keyless entry & alarm remotes. Newer ones don't use 23A batteries anymore so not sure what else uses 23A batteries.
I'm surprised you are having trouble with the Mitutoyo. Although I use the Folwer one more often I have PEC conventional edge finders & I trust them more. The Fowler one I use a lot cause they're quick & good enough (accuracy) but mainly when I don't want to mar the finish of a finished part. Useless for non-conductive parts or when I'm using something to protect the parts when clamped. But a jumper takes care of the latter, I'll just use a scale to complete the circuit cause it's always around. I'll use a conventional anytime the accuracy is more important, they're more accurate than the Fowler/SPI.
There's 2 models that Fowler/SPI offer though. The other one is the break away ball tip type that costs more than double than the standard one. Not sure what battery those use though.
View attachment 308045