I have been employing up to 100 people doing variable hours for the last 14 years (not in aviation). Two things are important.
1. Nowadays the 'self employed' status is not always valid, particularly in conditions where an employer is the 'main' employer of a person. It does not automatically allow avoidance of NI, tax or any employment legislation issues and employing staff on a 'self employed' basis cannot be used by an employer to evade these. The relevence of this to an employer is that they may have a responsibility for payment of income tax and NI even if staff are classified as 'self employed'. The relevence to a 'self employed' person is that they may still have the full protection of employment legislation including the right relating to unfair dismissal.
2. Where an employee is requested to attend for any period of time (and this includes being 'on call' even if this is in the employees own home) then at least the minimum wage must be payed for the full period of time requested.
I say may above because situations can vary but there are important issues to anyone who uses the 'self employed' method of paying staff, especially if this is done as a way of avoiding tax, NI or employment law issues.