Funny you should ask. I do keep a gun toolkit, not in my range bag, but in my trunk. Full set of gunsmith screwdrivers, 2 sets of small wrenches( SAE and mm ), small brass hammer, several sizes of punches, 2 sets of allens ( SAE and mm ), a ton of other allen and torx (sp) wrenches, Hoppes #9, a few patches, jags, rods, oil, etc. And some other things like pliers, etc. Just things I had spares of. Had a failure once at the range early in my shoot and had to go home to fix the problem, taught me quick to keep tools handy.
Well, I do actually carry tools in my range bag--though not an actual "kit." The socket sizes that hold my scopes on, allen wrenches for scope mounts, a spare battery, oil and a microfiber cloth, a #1 regular screwdriver for scope adjustment and a knife. Those are some of the basics that I've found come in handy.