Dr Red...
I must say it seems to be poor human factors design for the system to announce some pseudo-cryptic code, "T6NL," instead of something more intelligible -- e.g. "Warning, Engine Overheat" (for instance). But perhaps I'm being too picky.
I think you are being a bit too picky... The T6NL is a "caption" extermely well known to any Hawk pilot (must be if I can remeber it all after all thes years!), and all "bitching betty" does is restate the (prioritised) illuminated captions. Since the pilots would "know" well what T6NL means, seems fine. "Engine Overheat" is misleading, since there are other "overheat" type cautions often present, and why confuse with the "panel" saying one thing, and bitching betty another? In addition, any Hawk pilot will have heard and practised the consequences of T6NL every Sim trip... I certainly did (albeit pre the voice call out).
Incredible video of an extrmely well handled emergency... Just watch the flying pulling up to, and then maintaining exactly 125K - 130K, whilst trying to restart, turning back, briefing other pilot, R/T call and ejection. The "pitch down" at ejection is interesting to those of us (still) flying "light jets" when considering the effect of 1 ejection on the remaiing pilot / seat v parameters... an education