Do they have to pay me for back pension if I am found eligible?

Yes, if you are found eligible for back pension, you should be entitled to receive retroactive payments for the period you were eligible but did not receive benefits. The amount you receive will depend on factors such as the start date of your eligibility and any specific rules governing back payments in the pension scheme you are part of. It is advisable to consult with the relevant pension authority or a financial advisor to understand the specific details of your situation.