Flyer,
The only 'eligibility' you require for a BA command course is the correct seniority to be 'eligible' and the bid 'in' to request it.
There are alot of pilots who wait longer for their command as they wish to move directly from right to left on the LH fleets and others who jump at the SH commands as soon as their time comes up. There are no specific 'requirements' apart from having an unfrozen ATPL. Which you will need anyway for the LH fleets. The only entry requirements to LH are the ability to complete ZFT which requires a certain number of hours on aircraft over a specific weight limit (I can't remember the figures I'm afraid) and the ability to act as PIC when the Captain goes to the bunk.