Years ago I made a simple tool to do a similar job. Selected a piece of .040 music wire and cut to arbitrary length, say 1 1/2". Ground ends flat-ish and square-ish with a Dremel tool. Removed any burrs by a light stoning. Selected a piece of 1/4" x 1/4" square brass about 1" long. Drilled brass at centre of one face .045" dia. thru. Drilled and tapped #4-40 at centre of face 90 degrees to drilled face, so tapped hole intersects drilled .045" dia. Made a small knurled setscrew threaded #4-40. Put wire in .045" hole, installed knurled setscrew in tapped hole, and there it was, a custom mini depth gauge. No fancy finishing was done, and no high precision machining was required.
In use, the brass face is placed on adjacent face next to hole or slot to be measured, setscrew is loosened, the wire pushed to bottom of feature to be measured, setscrew tightened, then vernier caliper or electronic caliper or scale is used to measure from end of wire to face of brass for a pretty accurate depth measurement, depending on operator's "feel" for the wire to hole interface.
I've used this simple crude gizmo many thousands of times, it's surprising how often it comes in handy. JD