You may want to check who made the maps and the date. The Trinity Heights connector was constructed in the early 1980s as a link of the A.T. and since then it has been the official route. If you check the Crawford Path sign near goofer point and the Trinity Heights Connector sign near the corner of the Tip-Top house, you will see the A.T. logo. Check the Gulfside between the Crawford Path and the junction of the Trinity Heights Connector and the Gulfside and you will see which way the A.T. goes. The attached photo is from a vintage official A.T. map (revised 1983) and it clearly shows the only route as being over the summit.
Knapper-"The A.T. according to our official maps, split with two options, one has you bypass the peak on Crawford Path and turning left on Gulfside Trail (if you are heading north)."