I'm no fighter jock,but I also go along your lines. Recently since flying in these hardcore servers,like RAF nd war I've tried to copy the guys I normally watch flyby while hanging on my chute wondering 'I had him on my radar,locked,then he disappeared only to yell ''Boo'' from behind me....'
What I found was,or at least I think,is,once you get a radar contact (enemy),go TWS to determine their bearing (direction of flight),switch off your radar,dive to lose them,try to flank them meanwhile switching to boresight and furball mode,turn towards where they might be (assuming like the old me,they kept flying leisurely on after that spike). Chances are you'll be close enough to them for an auto lock and fox 2 or 1.
Now,doesn't their chute look nice against the setting sun :). I fly the F-15C mostly.