How do I locate a short in my Toyota's electrical system?

Brilliant, but hokie.

Disconnect the positive lead from the battery, get an ohmmeter and look down the positive cable while not connected to the battery. Wiggle all wires looking for a change in the reading. Try with ignition switch on then with it off.

Sometimes the battery wires rest against the exhaust manifold and cook through while slightly touching metal, this causes intermittents.

Try pulling all fuses except ignition and see what the battery drain is, then add each fuse, you might find the culprit that way

Your solar panel diode robs you of greater than a half volt charge from your solar panel so instead of say 13.8 volts you might be charging your battery at a real 13.2 volts.

.

Usually, you pull the negative battery off and connect a test light or voltmeter between the cable and the battery to check for a large draw and start pulling fuses until the large draw goes away...that indicates which circuit has the short. Most modern vehicles have a small parasitic load so there will be some draw of a few milliamps. Then it's a matter of tracing the wiring for that circuit to look for evidence of the short such as grounding wires or traces of arcing. It sounds like the lighting circuit is the problem...start with the ignition or headlight/dimmer switch and it's associated wiring/connectors. Check for bad grounds also as they may be causing the current to seek another path. Eautorepair.net has wiring diagrams...small fee.

Sounds like a connection @ the battery - NOT the terminals. There is a fuse link close 2 the battery & also a buss connector that supplies voltage inside. SHORTs blow fuses - are we talking short or an intermittent electrical connection ??Have U checked the GROUNDS ?? engine to frame - frame to body - battery to BLOCK..U could b breaking ground instead of losing your 12 volts !

sounds like a ground problem to me, the ground going from battery to chassis is important, clean under it and make sure it's grounded, you have several circuits doing bad things, doubt if you have a short in each and every one, sounds like ground.

you can't, you need to take it to an automotive electrician NOT a mechanic