Haha! Yes, they're hard to find. It's one heck of a nice, precision injection-molded part. That's why you can't see it. I have three of the 500 Series.
The black, ridged plastic thumb grip is the battery cover. It has a catch at its top, the top being the uppermost part as you look at the LCD. Push the upper edge of that ridged piece and simultaneously slide it down.
If you still have trouble, email me and I'll shoot a photo to send you.
I don't get it, Marc. You said a 500-421 Mit caliper, right? I have three of them. They all have the battery in the same place. I also have the Mitutoyo instruction sheet for the 500/550/551 Series, Manual No. 2035, and it shows that all of them have the battery in the same place.
Where's the reading skills problem? What did I not see?
Marc, I just scanned the English-language portion of the instructions for your caliper, plus an illustration of the battery cover removed from the caliper body. If you can read compressed TIFFs and you want them, let me know. If you need a GIF (no JPEGs of this one -- the text would turn to mush) let me know and I'll convert them.
Also, I have diagrams and text on the digital output formats, if you want to play with that.
Mitutoyo was my client for years. There's a photo of my hand holding your caliper on an old Modern Machine Shop cover. d8-)
Eh, no, Marc, and that's my fault. I've been getting real sloppy lately about posting my full sig, which says to delete the "3" from my email address. I just haven't wanted that much email...
If you want, try it again. Meantime, I'll send you the manual pages. Even if you have a unique Model 500 , they may be useful.
Again, let me know if you want the digital-output specs.
Oh, BTW, if you went to Mitutoyo's web site and looked at their little message board, you'll see that you aren't alone, finding the &%#@** battery cover on those things is a common problem. It always has been, ever since I got my first one around 1985.