Somebody once said the Hickok 1605M was a clone of the HP 410C, made to meet military second-source requirements. You might therefore look at the documentation for the 410C, free on the Boat Anchor Manual Archive (
www.bama.edebris.com), and see if it is close enough to your meter. Note that two versions of the 410C exist. The early one uses a single 12AU7 and some transistors; in the later one the tube is replaced with more transistors.
Otherwise, vintagemanuals.com can send you a top-notch reprint of the 1605M manual, for a price. Note that I have no affiliation with the company, except as a satisfied customer.