(When installing or removing jumpers, the amp should have been off and cooled down which makes it possible the electricity harboring capacitors have discharged. IF you shut off the amp with music playing, it will continue playing music while the capacitors are discharging.)
It seems you are probably on the right track for moving the jumpers.
When I turn my version of the MKIII upside down (removing the tubes makes the job easier for me)
with the volume knob pointed toward me, both jumpers should be connecting the two pins to the left for EF95 mode and vice versa for EF91/EF92 mode. When I look with a flashlight, 5654 i.e. EF95 appears near the Leftmost jumper pins and EF91 or EF92 near the rightmost jumper pins.
There are different versions of the MKIII. They do not all look the same when it comes to jumpers. With a flashlight, one can probably find the version number by looking through the housing holes when it's upside down. If you don't already have a manual knowing the version might help if you opt to look online.
It is common for people to lose hold of a jumper when trying to install it. Turning the unit upright and shaking can get it to fall out. Having spares can be good. Some people have bought aftermarket long-handled jumpers. I install the standard tiny jumpers using cotter pin pliers which are like a needle nose plier but much, much narrower, even narrower than tweezers, and not stout.
(IF the jumpers are installed for EF91/EF92 and one powers up the unit with EF95 tubes, the amp will not work and should be quickly turned off because one is shorting the EF95 tubes and probably risking other problems if left on. It is a somewhat common error and people have shut it off soon enough to avoid damage. IF the jumpers are set for EF95 and one powers up with an EF91 or EF92 tubes, another somewhat common goof, the amp is likely to work well but may risk being unstable with some tubes due to an unconnected grid in the tubes. In addition when running EF95 tubes in my MKIII, per my user manual, it makes no difference whether the jumpers are installed for EF95 or completely pulled out of the unit. I think of installing them in EF 95 mode as a good way of storing them and avoiding losing them.)