You know, the first A2000 I picked up about 6 years ago had something like this on the motherboard when I opened the machine up. It was located along the lines of resistors and ceramic caps, I think, if memory serves me right, on the far left side of the motherboard near the slots. I wonder if that was from the same thing. Regardless, I let some 99% isopropanol soaked paper towels sit on the involved areas of board for a while (maybe 30 mins or so), which broke it down a bit, then I used some acetone and a toothbrush to scrub it loose, followed by a wash with Dawn dish soap and a toothbrush and a deionized water rinse. A perfectly clean board was the result.
Remember that old rule of chemistry... like dissolves like. So you'll need organic solvents to remove the rubber (alcohol, acetone, others), then a detergent, which is bipolar and attaches to both hydrophobic and hydrophilic molecules (organics and water) simultaneously, which allows the deionized water to float the dissolved rubber/solvent conglomeration and their residues away after the cleanup.