On my 125HP 1995 mariner, battery positive comes direct to the bottom big terminal of the start solenoid. Should always be 12V there. When checking in the engine use the engine metal as ground. Up at the key switch try to use the engine metal as ground if your leads will reach or an extension wire, or first check the continuity of ground from the black terminal at the switch back to engine ground just to be sure the engine to key ground (black) is good (very low ohms, like 0.2 ohms).
Try to trace down where you lose 12V. From the starter relay post which is directly connected to battery positive, a red wire goes to inline fuse, then from fuse to the plug harness, then from this harness up to the key switch (red wire). Should be 12V at all of these places including the key switch red terminal. If not then bad connection, bad fuse, or bad wire, or (if you're losing it at the key switch and using black key switch as ground, in the engine to key ground path.
Stupid question but did you tighten down your battery connections?
