Re: what's draining my battery
First of all disconnect everything from your battery.
For several days, at the same time daily, take your multimeter and put it on dc volts and measure the batteries terminal voltage. If fully charged I like to use the number 12.75. If you are below 12.5 charge the battery, wait a couple of days for it to stabilize from the charging and retake the data.
If the several day test indicates that the voltage remains constant (within 0.2v is a good number) then consider the battery good and move on to the wiring. If not, get a new battery.
Elaborating on Bruce's suggestion per your comment:
Electrical current is "the water in the pipe" that moves energy (power when dissipated) around electrical circuits. The battery could be considered "city water pressure". If you have a pin hole in your water pipe, the water squirts out the hole and can be measured with a flow meter (in the pipe) as to how much you are loosing.
Electric current is the same way. You have a "hole in your pipe" somewhere and you need to find it. The electrical flow meter is called an ammeter.
Your multimeter should have two sets of scales for amps, or amperage. One is a separate plug that is for high current (10-20 amperes). The other range(s) are for milliamperes (.001 x amps) which are small loads. Probably 2 or 3 selections there.
The meter is hooked in series with the load (just like you would put a flow meter in a water line and measure flow) and measures the current (water) flow.
Problem with ammeters in multimeters is that being in series, they have internal measurement components which get hot, the higher the current, the hotter, and you have to get rid of this heat (dissipate it) without overheating the meter or other components therein.
I'd start with the special high current jack/ground connections (assume you have an electronic digital meter, not analog). Plug your meter leads there. You may or may not have to change your range selector switch. I think this is a separate circuit and you just plug it in and read....haven't used one in a very long time. Don't worry about + or - as that depends upon which way you connect your leads and your digital meter will measure either way. If you were to use the milliampere scales, you move your red lead from the high current jack to the V-R-A red jack that you use for everything else. Then select the highest milliampere scale and work back.
You probably will be using the milliampere scales as 3 weeks is a long time to drain the battery, so your leak is pretty small.
Reconnect all ground wires onto the - battery terminal.
Connect one lead of your milliameter (highest scale......200ma or 400ma type thing) to the + terminal of the battery.
One at a time, with all switches in the position where you get the discharged battery, take the other lead of your milliammeter and touch each lead that is normally connected to the + batt term, one at a time.
So we have the + battery terminal to one lead of the meter, thru the meter, out the other lead and onto the individual wiring circuits.
ANY reading on the meter is leakage and that circuit needs to be investigated. Since you are measuring the wires one at a time, the circuit with the reading is the circuit discharging your battery.
On the engine connector, give it time for the electronics packages to charge up (will get a current reading initially and it will go back to zero) before you decide that you have a problem. 30 seconds ought to be an adequate waiting period.
Need more, ask.
Mark