Well, it could be most anything.  Could be something as simple as improper carb/ignition sycronization.  Some of these engines had the “economizer linkage” (not sure if this one has it though).  If that feature is misadjusted, the carb might open way too early causing it to run lean.  Just because the carb “looked clean” doesn’t mean it is working properly.

The engine may be losing spark on one cylinder, or have erratic ignition at lower RPMs as well.  That feature you mention with the hose is the ignition system vacuum switch that prevents the engine RPM from running away when you cut the throttle back quickly.  This could be malfunctioning causing the engine to lose spark on one cylinder when the throttle is cut back.

The biggest thing here is to determine whether the ignition or fuel system is causing a problem.  Any way you can post a video of the engine misbehaving?  I realize it won’t post hear because the file is too large, but maybe you can post it on youtube.  You can even send it to me through email if you like.

Finally, I realize the past owner had rejuvinated this engine, but it is possible that is has poor compression, or perhaps water leaking into one/both cylinders.  It only takes a few minutes to check compression and doesn’t cost anything to check.

To echo what fleetwin noted, your motor is equipped with the “fuel economizer linkage” and you might check this linkage for proper adjustment.   I’ve attached a picture from my 1956 Johnson 30hp which should be identical on your Evinrude.

To adjust the linkage with the engine off, shift the motor to forward gear and advance the throttle to fast (wide open) throttle.    Referring to my picture, with the throttle wide open the armature bracket should be touching up against the crankcase stop.   At that point, the link rod collar should be snug up against the pivot pin on the throttle link arm.  If not, loosen the rod collar screw and adjust it so it is up against the pivot pin with the armature bracket still snug against the crankcase stop.

As David, fleetwin and Dale also noted, there could be other issues causing your running issues.   Check compression and check for proper carb adjustment, good hot ignition spark and possible ignition grounds.   We are here to help.

see pic  of low speed   fuel path and drip chamber  fed by that narrow  fuel  channel up the side ls  channel

see fuel saver info if applicable… to your Evinrude cousin… it is the type of info available all across that 400+ page book coveing carbs ignition, gc etc.. etc…

keep in mind fuel flow is critical  anything  affecting the operation of tank pressure system  and fuel flow ( via filter)  may only show up at lower rpms.  see manual

BTW    tank runs with fumes inhaled  doesn’t always help…