Thanks DigDog that helps some. So it sounds like level 3 might not be on-call as the resolution time might be a couple days or so.
Do not make that assumption.
It all depends on the organization, the layers involved, who owns the layers, who developed it, SLA'a etc etc.
Lets look at a variation (building off digdog)
T0 - Self help. AKA check the wiki\faq
T1 - Call center whose responsibility is to capture the information, log the issue and have access to VERY basic activities that are covered in a predefined script.
These 2 layers can generally be automated or converted to basic AI. When shit hit the fan, there isn't much value to these folks staying on a triage. These folks are glorified data entry.
T2 - Call center where someone has big picture of issues going on or junior in house person. They have read the troubleshooting guide a lot and have a vague idea of how things work. This is the typical the tier where people will own the problem and work towards resolution.
T3 - This is typically a Subject matter expert who will work with the T2 to work towards resolution of an issue that falls outside of the standard scripted stuff. This can be everything from DBA's to developers to platform people.
Both these tiers can end up on call. Both those tiers can end up on 14 hour bridgeline to deal with someone else's f00kup.
T4 - Senior T3 (Senior devs, DBA's, generalists who have seen some shit), Architects who have to organize\manage\direct all the different players to put all the puzzle pieces in place. These folks can still get pulled into a call but they are the ones who hop on...layout out the game plan and hop off once everyone is clear on what next steps are.