After a little more research maybe it's a bad ESA? It does shift into gear, just shifts hard. The cable seems a little stiff and should probable be replaced too.
Howdy,
Welcome aboard!
It'll help if you post your model number. There were quite a few models in 1994 and 1993.
502ACPMDA 1994
502AGPMDA 1994
50FACPMDA 1994
50FACPMDM 1994
50FAGPMDA 1994
50FAGPMDM 1994
502APLJVB 1993
502APRJVB 1993
502BPRJVB 1993
50FAPLJVB 1993
50FAPLJVN 1993
50FAPRJVB 1993
50FAPRJVN 1993
Now, you said you have an SX. If true, Jammer is right. there's no ESA. If you do have an ESA, you do not have an SX.
Now having said all that, unless you bought the boat new........ Many things can have been changed/modified in 23 years.
The idle for a 94 5.0FL is 550-650 RPM. I would tune it for smooth idle and an in-gear RPM of closer to 550. Higher RPM's will eventually damage dog and cone clutches.
The ESA on a dog-clutch Cobra is there for getting it out of gear and doesn't (and shouldn't) activate going into gear.
Once you determine your model number for sure, I would suggest you obtain an OEM service manual (not a Seloc or Clymer)
In the mean time
http://boatinfo.no/lib/omc/manuals/1986-1998omcmanual.html#/88 is pretty good.
Cheers,
Rick