Sticky residue is normally the flux. IPA doesn't dissolve flux, it just makes it runny. So if you gently wipe it off, all you are doing is smearing flux everywhere. Once the IPA evaporates, the flux turns into a horrible sticky mess.
The solution is to add a bit more IPA to the board, wait a minute or so for it to soften the flux, and then using something like kitchen roll, wipe in small circles, changing which bit of the kitchen roll you are using as you do (so that you don't smear what's already been wiped up back onto the board).
For intricate places around ICs, you can use the same process, but rather than wiping the kitchen roll on the board, use something like a pair of tweezers to push the roll down on the board and move back and forth around and between pins.
You should find the areas that have cleaned well stop being tacky. If you find anywhere that is still a bit sticky, then simply repeat the process.
What is also worth doing before you start cleaning with IPA is to gently chip off any really large blobs of flux - you can usually do this with a blunt instrument and as long as you aren't jamming something into the board it won't do any damage to the solder mask. The advantage of this is it means less flux on the board that has to be wiped off after it has softened up, so less that will smear around everywhere.
I've used OSH Park before, and never had an issue getting the boards clean with IPA and some elbow grease. As to why your particular board is being more stubborn to clean, it happens from time to time. Maybe you had ended up with more flux on the board, or when you were wiping off the IPA you used something that wasn't doing as good of a job of absorbing the grot. Could be many factors.
From the circuit, it appears to be a transistor. By using a DMM in diode test mode you might be able to determine if it NPN, PNP or shorted or measure voltages when active.
Not listed here
But possibly a PNP here
Best Answer
It looks like a bridge rectifier but I can't think why there would be one in a 12 V DC circuit.
simulate this circuit – Schematic created using CircuitLab
Figure 1. A bridge rectifier consists of four diodes.
There's no scale reference in your photo but I'd guess that's a 1 A device and so is unlikely to be in the actual indicator lamp circuit as these are normally 21 W lamps drawing nearly 2 A each when hot and a lot more when the filament is cold. It's more likely to be rectifying the power for the flasher unit itself.
They're available from any electronics component supplier. You'll find a parameterised search on any of the large suppliers. Select something that's rated for 50 V and whatever current you think is required.