if you have good wires... sparks with the switch OUT then the switch is bad or wrong type.
it should NORMALLY OPEN when not pressed ... just check it with a ohmmeter.... don't assume we know what that does.
if relays click next step is to check what comes out to feed power to the t&T motor..assuming a 2 wire T&T check for +12 and ground to the trim motor via blue-green or your colors if different . up and down just reverses the power and grd. check fuses or any interrupt feature of...
see carb clean up ... remember yours has no needles just orifices the rest of the procedure is pretty much the same. for starter do not mess with the delicate orifice plugs other than a strong blast of carb cleaner followed by air blast ( a Dollar store keyboard spray can will do if you...
easiest is probably the carb.. it is an old style carb with even simpler orifices ( no long needles like shown in old carbs) for low and high speed.... easy to clean/inspect
with low experience your best best is to start by trying to clear gummed up orifices with a good blast of carb...
that allen head oil plug leaking may not be tighten down enough on a NEW NYLON GASKET ..
personnally I prefer slotted ones because the allen head ones s trip easier if forced. they are a pin to remove if stripped. you have to punch them out bacwards
check compression and... try to find a nice old shifter handle !
http://www.leeroysramblings.com/johnson_magneto.htm
Fisherman 6hp great little engines cheap on fuel smooth running
and easyto srvice... carb should be openned up and clean all passages...
The RK series gear case is extensively covered in the Johnson service manual (500 pages +) available for free download to members of AOMCI
in the "members only section" library under GarrySpencer's drop box
here is a example...