If you can tolerate a couple of seconds delay after pairing, a monostable would do the trick. Wire it so that when it's active it's providing the "off" output. Set it's interval to a bit longer than a whole on/off cycle when the b/t is un-paired. Then when it's paired the mono stops being triggered and the output stays high. A 74HC123 will do the job nicely. A 555 will do it if you can tolerate the output being the wrong polarity (so you would need to invert it).
Some people would be reaching for a microcontroller at this point - there are some 8 pin ones and you'd need no other parts so it's a tidy solution. Also there is the advantage you could program it to read the actual "connected" message from the b/t. Of course you do have to actually program it which might be getting too involved.