EICO 636 is the same as Realistic (Radio Shack) Model T-B-C (Tube-Battery-Continuity) tester, and also very closely related to EMC 211, 213 and 215. As far as I know, the last tube tester model EICO produced themselves was the 635, so apparently EICO (as well as Radio Shack and EMC) decided to out-source these models at their final legs of the tube tester business.
You can use the schematics and tube setup data from EMC 213-215 for your EICO 636. The complete document is posted on BAMA > http://bama.edebris.com/manuals/emc/
EICO 636 and Realistic T-B-C has a battery and continuity testing function in addition to the tube testing facility. EMC 211 and EMC 213 is a plane-Jane tube tester, and the EMC 215 has an additional transistor tester function. But the tube testing section of all the models are the same and the setup data are interchangeable. Use the EMC 213 schematics for your EICO 636.
Unless the meter and/or power transformer are dead on your 636, there isn’t much inside so it would be very easy to fix. Clean all the switch contacts and tube sockets with a contact cleaner that removes copper oxidation, clean the pots, replace any out-of-value resistors and a .02uf cap by the neon lamp, you should have a working emission tester in no time