Using the method you described, you should have had your voltmeter on an 'Amp' setting, and you would have read a current draw off the battery. Current is measured in series; volts in parallel.
I just went out and checked on my truck: on a battery charged to 12.8v, doing what you described yielded a volt reading of 10.2v, slowly climbing to 12.8v before I lost interest. Testing volts in that manner is basically reading the battery voltage through the wiring harness, and doesn't provide any useful information. You haven't hit upon your problem.
Check for a current draw, starting with the battery. Then check current draw on your relay, since you already suspect that. If the draw of the relay isn't nearly your total draw on the battery, then the problem is elsewhere. Current flow is a first-order effect, voltage drop is a secondary effect. (As an example, the stereo in my truck draws about 300mA even when off...running the clock, holding memory presets, etc.)
Think of electricity as water in a pipe...voltage is pressure (psi), current is flow (gpm).
Last edited by Shakey61; Wed Oct 09 2019 01:25 AM.