What are the jurisprudential rulings and the legal qualification of the relationship with the maintenance technician if the mechanic agrees with the technician and pays him his wages from his own money, and the mechanic refuses to take any compensation? And do the mechanic and the technician deserve payment for the repair that resulted from the disassembly and reassembly, or can the defect that appeared and was not present before be considered as compensation for the repair?

The mechanic bears the cost of the electrician because he was hired to fix the fault, and his seeking help from others is not your concern. It is permissible to agree with him to repair the defect, even if it entails purchasing spare parts or seeking assistance from others. It is also permissible to combine a lease contract (ijarah) with an agency contract (wakalah). The mechanic guarantees what he spoils because he is a joint agent (ajeer mushtarak). It is permissible for you both to agree on evaluating the fault and considering it part of the rental amount or forgiving it.