As with any reverse engineering effort it's probably a good idea to get acquainted with whatever information is publicly available for this device before ripping it apart blindly.

A Google search turned up a user manual but unfortunately no service manual. The manual shows that the microscope control box runs on a rechargeable Ni-MH battery. From the images it appears to be a 4-cell pack. This could be a clue to the operating voltage of the microscope (alternative there could be a boost or buck converter in the control box). It also details that the microscope optionally has a PAL or NTSC camera and that it outputs S-Video. So we can expect to find a video signal from the microscope.

Google also turned up a press release from the company that produced the miniature stepper motors that are used to drive the focussing and zoom mechanisms. It goes as far as listing which specific motors are used. From this we can assume that device generates two phase unipolar stepper drive signals somewhere.

A search on Google patents also turned up a couple of interesting patents relating to the device. These deal mostly with the optics and don't not provide a great deal of information regarding the electronics. They do mention that an Infra-red range finder is used to determine the distance to target for the auto-focus system. So that is another piece of the puzzle.

Links:

Leica HM500 user manual

Micromo application/press release

Micromo stepper motor data sheet

Patent US7286287

Patent US5971540