You don’t actually have to partition the SSD to use it for TimeMachine with two different computers. TM will ‘know’ which computer it is connected to and keep totally separate backups. That’s both good news and bad - you’ll be duplicating files and apps with two backups and there’s no getting around that.
We generally recommend the TM drive be at least twice as large as the amount of space being backed up and I like to make that 3 times to allow for growth of the source files. So figure out how much space both drives are already using, do the math and if that is close to the capacity of the SSD consider getting a larger SSD.
All that said, I don’t consider a single TimeMachine backup a total strategy. What happens if a thief walks in, takes both Macs and the hard drives and printer? This past winter it happened to my neighbor. I recommend at least two backups with one of them being off-site. To accomplish this I have two backup drives. One stays at home all week and goes into work on Friday. The other is in my desk at work all week and comes home on Friday.