Most amplifiers follow a common protection scheme. Basically, when there is a short circuit, or impedence too low for the amp, they cut out. That cut out may be a self re-setting relay but it's also been common for a fuse to be used.

My first thought is this. Your outdoor circuit may have a short somewhere in the wire run or, your using 4 ohm rated speakers and this amp is designed for an 8 ohm load. One simple way to test for this is to use an Ohm meter and use it to check for a short circuit. Unfortunately, you can't test the system impedence but it's pretty easy to spot a short circuit, just look for an Ohm reading under 1 Ohm. If the resistance is between zero an 1 ohm you have a wiring issue that needs to be corrected. Do that first so you don't risk further damage to your amp.

Next, test the A speaker circuit in the amp and see if it powers the speakers without faulting. If so, then the amp most likely has a short in the B speaker circuit, something that should be very easy to correct. My first suspect would be the terminal block for the B circuit, replace that and you may solve the problem. As for that amp itself, that may be a very easy fix. Some amplifiers were built with both a self re-setting overload relay AND a FUSE. What may be causing those flashing lights may be a blown fuse somewhere inside the case. However, the first thing I would try is unplugging the amp so that it is powered down completely then power it up and see what happens. Sort of a re-boot for the amp. Then, if that didn't fix it you can move up the list. If your handy, you can try removing the cover and look for a fuse somewhere inside the case, just make sure it's been unplugged for at least 24 hours. While your poking around, take a pair of reading glasses and look very closely at the terminals for the B speakers, sometimes a broken strand of speaker wire can cause a short, if you find something like this just tweeze the strand out of there. As for replacing the terminal for the B speakers, you can get parts like this at Radio Shack, however you'll need skill with a soldering iron to make the swap and it won't be an exact match to what Pioneer used. If you don't have that skill, it might be worthwhile to take it to a repair shop.

You didn't mention how it works when using only the A speakers or no speakers.