a.c. condensation thick brown goo.?

Your evaporator coil is probably filthy. The correct method is to remove the coil to clean it. Which is expensive. You can clean the coil while in place its just a pain in the ****. And is very time consuming, About the best thing you can do, is try with a soft nylon brush, is to brush the coils off as best you can. You dont want to really push on the brush, and you have to go the SAME direction the fins are running. They bend very easy. You'll also want to make sure the drain pan where the water collects is clean, personally I would use simple greeen. Its non toxic, so spray it in there and use a tooth brush and rinse with some water. A spay bottle will do about. Just make sure the water drains! If not your condensate pipe (the white pipe which is plastic) is partially blocked.

I gather you're talking house not car since you're in home and garden. If it's a central air system that has separate units, one outside and the other somewhere inside, then the 'sludge' is coming from the inside unit. Mine is in the attic. The technician showed me where to disconnect the drain pipe and pour bleach down there. You can have a bucket at the other end to capture it and use it again. I mean like right away! Pour it through several times then pour some HOT water down to flush it. You'll be surprised at the junk that comes out. Do it every spring and you'll be ok. As to what it is; I'll bet your system is at least 8 to 10 years old, at least, so I would say it probably is rust form the inside of a decaying evaporation drain tray. Also in addition maybe some kind of growth like alge or something. The bleach and hot water will take care of that. It probably just means that you need to start socking a little away every month to get it replaced eventually. Now if it is rust you can replace just the inside unit when it becomes necessary. The two units work independently, but together to do your system's work. So they don't both have to be replaced at the same time. Don't let anyone tell you otherwise.

When it runs the coil gets cold and condensation drips into the pan, not all of it drains immediately so it ends up turning into a slime and can eventually block the drain altogether.

The evap coil isnt necessarily dirty but the drain pan sounds like, it is. If you can access the coil(mounted on top of the furnace) you can open a panel and try to clean it out.

you have a dirty evaporator coil. change your filter. not a whole lot you can do about it. cleaning an indoor coil, if done right, is about as expensive as replacing it. you have to evac the system and take the coil outside. i know someone is fixing to tell me i'm wrong, but i don't like that coil cleaner. and maybe you can lock the refrigerant up in the compressor or condenser so you wouldnt have to evac, but on a residential unit? FOR REAL?

just let it go. change your filter and poor some bleach down your primary drain.