For US 121, there are just a few operators that hold ETOPS 240, or greater. The two TLS are cargo fire suppression, and other than cargo fire suppression. Those certfiied durations (in minutes) would have to be stored in the aircraft tail database. 777, 787 and A350 are all the types I am aware of that can do this.
Here is an ETOPS summary for a 777-300ER, SCEL-YSSY, at 240. Under 121, you can get 240 minutes as the initial application, do that for a year, then you can go to whatever circle the aircraft is approved, say 290, 330, etc. Because at 240 this routing is limited in this city pair, I must cross what I call “the corner” between the SCIP and NTAA 240 minute circles, at 40S140W (40W40), and can optimize the rest of the route. So this route today becomes DGO6 DGO DCT 3580W 3790W 38W00 39W10 40W20 41W30 42W40 43W50 45W60 46W70 45S80 DCT OKTOM L508 CH N750 PLUGA M636 TESAT. At 330 SCEL-YSSY, I can fly essentially a great circle, and brush the north coast of Antarctica. Of course this route and ETD assumes that SCIP is available H24, which of course it is not.
All the standard ETOPS rules still come into play, and is at the top of this ETOPS summary. But in this simplified display, we calculate with all of the ETOPS airport pairs (SCIE-SCIP, SCIP-NTAA, NTAA-NZAA, and NZAA-YSSY) the divert times for the time limited system scenarios, but just display the most limiting. These are calculated at the operator’s engine-out speed (354 KTAS, for the latest arrival time at the alternate), then the earliest arrival time (flown at a high-speed cruise, like 489 KTAS here).
The fuel burns shown here at the bottom do not include any of the ETOPS Crit Fuel Scenario additives as you already added that gas in the sections above. For US operators, only AA and UA hold 240 or beyond. In TLS considerations, all you are worried about now are Time, not fuel, and unlike the static circles, these times in the TLS scenarios are based on the forecast winds and temps of the day.
For US ops, its eCFR :: 14 CFR 121.633 -- Considering time-limited systems in planning ETOPS alternates. (FAR 121.633) The Boeing ETOPS Guide, or Airbus’ Getting to Grips with ETOPS, are what I consider as essential to understand the nuance of TLS operations.