WR 800m pace (1:40.91) averages 50.46 seconds per lap.
WR Mile (1609.344m) pace (3:43.13) averages 55.46 seconds per lap. For reference, 1500 WR pace (3:26.00) is 54.93 seconds per lap.
Average 800/mile WR paces together and you get 52.96 seconds per lap which equates to around a 2:39 1200 for the world record. This is just shy of 1K WR pace which is 52.78 seconds per lap, so maybe add 1 second for the WR being 2:40ish (53ish per lap).
The fastest 1200 ever recorded was supposedly by El G, who ran 2:44.75 en route to 3:26.96 in the 1500. However, this could 100% be beaten in a standalone 1200m race.
If the 1200 was an event, my guess for WR holder would be Noah Ngeny. He was a 3:43 miler and a 2:11 1K guy. Just like the 1000, the 1200 would be a middle ground race for 800/1500/mile specialists. The 1000 would tailor to those better at the 800, while the 1200 would tailor to those better at the 1500/mile.