Yes, Argentinian accounts state that Ardiles' wingman went u/s and he carried on alone. He was in a Dagger (former Israeli built Mirage V - Nesher) and unsurprisingly carried the Israeli made Shafrir 2. So that's what Ardiles launched and not a R550 Magic. However, the Shafrir 2 was an AIM-9D/G class weapon and also comparable to the french Magic and although a good missile it was certainly inferior to the AIM-9L and more importantly
did not have ALASCA (all-aspect capability). Therefore, Hale logically elected to get out of the way when he saw a head on missile as he most probably would not have known whether it was a radar missile-equipped Mirage or an IR-missile-carrying Dagger. Whether Ardiles launched while having a good tone..well it must be a moot point. No ALASCA-no joy!
Why did he shoot? Well scare tactics come into mind although he doesn't seem to have come into the fight full-hearted as apparently he then proceeded to light the burner present aspect by turning to escape and in doing so presented a good IR source to Penfold.
What is curious to me though is that several reports (apparently originating from Hale) said that he was being tracked or locked up by that missile. Since as you've said he never had any indications of RWR he definitely did not have a radar BVR missile on its way to get him (which a Dagger didn't carry anyway). My only assumption (again!) would have been that he got a smoke trail coming his way which had been fired without lock; he took evasive action and in doing so presented a heat source (as he went from head on to a vertical dive). But I am not sure if an IR missile would actually do that. I know of LOAL capability of modern fire and forget IR missiles but I wouldn't know whether a Shafrir 2 of a couple generations back would be able to do that i.e., get launched in the general direction of a target without lock then as the target's heat signature is presented it locks on to it in mid flight! I mean Martin Hale apparently (in terms of what he saw) was convinced that the thing was tracking him! Which in simple technical terms couldn't happen (no head on launch capability)! So how is that possible? (Unless of course - and that yet another scenario
- the adrenalin factor made him conclude that it was tracking him when it was not). Again all available reports state that the missile actually "ran out of steam" before getting to him and he'd dived several thousand feet! Now there's a mystery!