My throttle/shifter single lever combination is a Morse from 1972, sorry, no model number. My symptoms were engage the tranny at 1000, not while idling at 600, 1000 rpm engaged, or 1500. Being new to diesel boats it didn't seem odd to me, and two professional mariners didn't mention it either, but idling at 1000 equals 5k speed. Some low speed control problem. I tried all manner of dockside fixes to resolve the problem, My engine was either idle neutral, 1000 and 5K or 1500 at 6.5k. No professional engine person I talked to had any idea, none admitted any knowledge of the Morse single lever control.
I finally bought a new Morse cable, I tried to fit the ends exactly the way the old cable was, the problem was worse, engage the tranny at 1200. I went online to find some information about the cable adjustments, but got only vague hints, but I came up with an understanding of how that system works. It seemed the cable adjustment was too tight, even on the old cable, with the cable adjusted properly, it no goes into get while the engine is at idle, I can then raise the rpm to 1000, but anything between 600 and 1000 returns to 600 when I let the lever go. I decided this is a brilliant bit of the throttle lever design, allowing for a quick low speed thrust with idle return for low speed maneuvering.
The new cable moves a slight bit easier than the old cable, my problem was completely in the mis-adjusted linkages on both the transmission and throttle.
Based on my experience, I am betting your problem is a loose connection on one end of either cable.
