hmm, splined coupling not a 'lovejoy',probably on a flexible shaft.
I've never done one but...
I'd mix ATF with acetone (50/50), then pour it into the grooves and splines at the coupling,'flood it' ,wait a few hours, do it again, several times. The idea is to have lots of patience to allow the ATF/ace combo to work it's magic. Any kind of thin 'penetrating' oily stuff will work, though it takes longer in the cold.
The coupling looks like a long springy cable , but it will come out when you pull the pump out.
While you're in the neighbourhood, waiting for the 'magic', scrape out most of the grungy gunk that's laying about. Once you've installed the belt, reinstalled the pump, spray some 'oil' onto that 'springy coupling' section. That actually would like some oil.
Depending on how the pump's mounted, put a box or shelf to support it. I'm thinking the coupling overlap would be 2 inches( ? ), so when you tug, tug on the pump, be careful you don't go 5 or 6. it might come free real fast ! When you reinstall, add a smooth layer of never seize on both parts, wipe off excess,so it doesn't splatter onto the new belt, making it slippery and forcing you to do it all over again.....