First, verify the obvious: That the 12vdc supply can provide the greater than 2 but less than 3 amps needed to power the transmitter. Use a current meter in series with the supply to verify the current draw.
If the supply is capable (more than 3 amps when transmitting), I would start by separating the Power Amp (PA-brown wire) supply from the main board supply (red wire). If the supply still dips, then the finals are not likely part of the problem. I would then check wiring of the PTT and key to make sure you are not shorting the supply there.
If the supply does not dip, then the PA circuit is the problem. You will then need to go through checks using the schematic.
In all cases, make the transmissions as short as possible to try to keep from damaging components.
Verify the above and get back to the group with any findings. We will need more information to provide more help.
73
Evan
AC9TU