There is not set procedure it seems. Convention says that after eligibility met, it goes for BG check as service agent said. Perhaps, an officer at the end go through all the recommendations (including eligibility) on the application before giving a final green flag. Eligibility status only changes on profile in the end, not before (so could be anywhere in the process). What matters is recommendation 'met' as most likely officer will follow that recommendation. Hope this helps but I am not expert as in the same boat as you.