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.