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Saying you're down to do something means the same thing as saying you're up for it.
(discuss.tchncs.de)
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
It makes a little more sense with the context that “I’m down” is shortened slang for “I’ll throw down on that”, itself slang for “I will get in on this situation” (as in “throwing down” some money or chips when gambling)
I thought it is short for "I am putting myself down for that" or "put me down for that". As in, putting yourself down on a list for attending an event.