Joe,
Timeout value is configured in "persist add uie" command in seconds.
E.g. when you add a persistence record to the table you define how long it should live there.
In your case for example for a 10-minute (600 second) timeout :
persist add uie [HTTP::cookie value "JSESSIONID"] 600
Re: persistence not working - make sure you have OneConnect profile enabled on the virtual server. Without it the load-balancing decision is made upon the TCP connection (e.g. way BEFORE any cookies can be read).
Here is the KnowledgeBase article for your reference:
https://support.f5.com/csp/article/K7964
Hope this helps,
Sam