This is an issue very common on the SE/30, but the OP mentions an SE/20. Everett--is it an SE/30 or SE/20?
To tell them apart--
* The SE/30 is the model with the 68030 processor. Most are marked SE/30 unless someone did a logic board swap and kept the SE's original bezel.
* The SE/20 is NOT a machine with a different processor. Instead, it's simply any Macintosh SE with a 20MB hard drive installed. This was a common marketing term back when the SE was new. At one point, all SEs had 20MB MiniScribes (this changed later in the computer's production run), so if the machine was a stock SE/20, it meant it had a 20MB drive, not a 68020. These computers are never designated SE/20 on the front bezel as the SE/30s are. (The 20MB sticker was on the back for US versions, and there was typically something like 1/20 on the front in some countries--but never "SE/20").
Basically, the SE/30 is its own model with its own processor, RAM upgrades, specs, etc. The SE/20 is a way to refer to a Mac SE (regular model) with a 20MB hard drive.
The reason this is important? The SE/30 is notorious for leaked caps on its logic board, but the SE doesn't have the cheap caps of its more powerful, initially more expensive brother.