I'll toss in my 2 pennies.. in my experiences thread chasers are a waste.

The aluminum head probably galled and welded to the tap, always apply a lubricant and not "Tap Free", especially when working with Aluminum and Stainless Steel.

"Tap Free for ferrous metals", and "Tap Free for Aluminum" work well when cutting threads. for chasing threads, I just use wheel bearing grease 'cause the junk clings to the grease and helps clean the bore, just blast with air after and the junk and grease all come out. I've been known to use my old 9 volt makita cordless drill, set the clutch to minimum and using low range have at it. Skill or luck..??..? who cares! I haven't broken a tap in years.

For all stainless fasteners and aluminum parts make sure to use an anti sieze, if you don't have an anti sieze or any lube, you can actually use toothpaste, while I've never tried it.. it supposedly works well.