The mileage counter is mostly mechanical. The only electrical part is what times the light's duration.

I mentioned the broken spring post as the common failure. The counter is driven by the decade shaft of the odometer to which the hundreds digit is fixed. A worm gear turns a simple optical encoder gear which has a cam hub. The white area on the gear keeps a phototransistor turned on until it rotates 5K miles worth and the black area is in front of the reflective sensor. That triggers an electronic timer to turn on the service indicator lamp for a short duration.

When you move the lever up, it disengages the worm gear and it should force the cam hub to its start position. You'll feel the "snap" as it sets the cam. The spring is supposed to keep the gear in contact with the worm driver. See http://cleanflametrap.com/speedo5/ for a better visual on this.
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Art Benstein near Baltimore

Free advice is sometimes worth what you pay for it.