Technician reported he replaced the Captain's yoke without a Required Inspection sign-off when it is required per the Aircraft Maintenance Manual.

Narrative

On Day 0 around XA:00 I went out to my assigned aircraft to work an MEL for a Captain's PTT (Push-To-Talk) switch being intermittent; I was not able to find the switch in the IPC (Illustrated Parts Catelog); so I discussed it with my crew chief that night that had stepped up to be a crew chief and he agreed with me that it was a control handle replacement. so; I went out and checked my IPC effectivity and then went out to the aircraft and went ahead to remove the Captain's control handle. after I removed it; I called my crew chief and told him i was ready to install the control handle and that I needed QC (Quality Control) out there before i started the installation since it was related to flight controls and the AMM (Aircraft Maintenance Manual) note up top said RII (Required Inspection Item). so he called QC on the radio and a QC inspector came out. I talked to him about what was going on and was ok with everything and I showed him the old control handle and I verified with him that the new control handle was effective per the IPC. i also showed him the AMM to make sure we were on the same page and we were and he was fine with it and I proceeded to installed the new handle he witnessed everything up to the torque and he checked my torque wrench and it was good and he made sure I didn't forget to fold the tabs over the screws heads and as i was installing the boot another QC inspector came up just to assist and he started talking with [the first QC Inspector] and they were discussing if the control handle was RII or not and they both questioned the job if it needed RII or not and they agreed that it wasn't RII but they called a 3rd person over the phone to verify if the control handle was RII or not and he also said no that it wasn't so all 3 persons said no and that's when I said ohhh ok and I trusted them thinking they were correct since 3 QC people said no and then they left since they came to the conclusion that it wasn't RII and I proceeded to finished the install.