Hello Doug,
Yes, as Jason said a static agent might work. However, if it doesn't and given that your question was about elastic agents, the answer would be "it depends on the elastic agent plugin". The plugin interface definitely has enough power to do this, since it controls almost all aspects of job assignment to agents.
For the Kubernetes elastic agent plugin, there is a property called "Maximum pending pods" which seems like it will do what you want. I think you should try setting that to 1 to see if it does. What might be confusing is that this is at a cluster profile level. So, it affects the whole cluster and is not at an elastic agent profile. So, in the worst case, you might have to duplicate the cluster profile itself and associate only that job to an elastic profile in that cluster.
If that property doesn't work for you, then you might need to look deeper into the Kubernetes properties you mentioned.
Hope that helps,
Aravind
PS: If the terms cluster profile and elastic profile, etc. are confusing, you're not the only one! There is some work being doing to improve the experience around this. For instance:
https://github.com/gocd/gocd/issues/6731. If you (or anyone reading) is interested to help with opinions and want to be guinea pigs for some quick research, I'd
love to hear from you.