If time is measured manually, it will be a "manual" tester.

Probably a slot machine would be more convenient, so that you don't have to keep looking to see if it has already run out or not. And I have an idea: to make an electronic circuit that consumes constant current and powers the clock (an electromechanical one with a 1.5V battery, usually works well up to 1V, and after a voltage drop, e.g. to 1.1V for NiMH, it disconnects from the battery. Charge the battery, clock set it to 12:00 (or write down what it indicates), connect, and if the clock is running, you will read the time and you will know what capacity - only because the clock shows the same time every 12 hours, you have to look at it a few times a day, to later know if the discharge lasted, for example, 10h, 22h or 34h. Or ... repeat the test a few times, with different discharge currents. Or - but this is a complication of the system, a bit difficult when supplying about 1.2V - to power the clock "in pulses" , turn on the power for a minute, then a 4-minute break (discharge current to keep flowing), then multiply the indicated time by 5.
Or the old method invented by Faraday: pass the discharge current through a "cell" with copper electrodes immersed in a copper sulphate solution (other combinations are possible too, but not all work stably, this one is good). Weigh the electrodes before and after discharging the battery, the difference is converted into capacity (need Faraday electrochemical constant F = 96485.33289 C / mol, copper atomic mass Ar = 63.546 g / mol, copper valence w = 2; capacity = m * F * w / Ar; approximately, 1Ah is 1.2g of copper, more precisely 1.1855g). By the way, you can sit something.
The current source from the LM317 needs over 4V for proper operation, so it is not suitable for a single Li-ion battery, or even three Ni-MH batteries.