It works! Everything's hooked up and it does what I expected. With chilled tap water I felt the cooling effect immediately, but of course with no ice it didn't last for long. That's a problem because the pump I chose needs to be immersed in water to work, and it takes up most of the space in the current coolant (water) reservoir, aka the thermos.
This means I either need a larger thermos which can fit both the pump & the blue ice cores, or I need to fit one of those USB thermoelectric drink chillers to the underside of the thermos lid with a heat sink poking out the top, and attempt a purely thermoelectric water chilling approach. Maybe both? That would be the only truly original thing about this project.
Upon googling "cooling vest" I have discovered the ice water ones are very common, cheaper than I believed (I bought a sample unit to copy design elements from) and there are even fully thermoelectric ones out there. It's actually a common thesis project for Indian engineering students, which makes pretty good sense given how hot it gets there.
Anyway I believe the USB powered chillers I can run off a solar charged battery (it won't run directly from solar I believe, without a much bigger panel) don't chill well enough to be the sole heat removal strategy. BUT, they might prolong the frozen state of the ice cores. This would be the first hybrid ice/thermoelectric cooling vest design anywhere, that I'm aware of.
More details in the coming video