First of all, after you have booked, see if aerlingus.com allows you to do it. BA will give you a PNR, what you then need is the Aer Lingus PNR which begins with a 2. You should see this on BA.com under seating, or it may be visible under classic.checkmytrip.com. However note that you will have to pay for specific seat selection, not that I would bother on such a short flight. If you pay for an emergency row seat then you also get Priority Boarding with the same fee.

Thereafter, yes by all means ring up, there are some threads in the Aer Lingus forum which may help with how seating allocation works there. I would consider getting the Aer Lingus app, particularly if you have further travel ahead, whilst not as good as BA's App, it is quite useful. I'm told they are trying to link seat selection in BA.com for Aer Lingus flights, but I can well believe this to be complicated. But if you can get the App to work, then if the flight is in the morning check-in after 21:00 hrs the night before, select "sit anywhere" and you should get a good seat. Evening flights you best do on the morning of travel.