It will require modification of the harness but this is not a major task if you research how it should be wired before you start. Can you describe the 350 a little? Does it have fuel injection? What kind of ignition is it running?
How long a harness will take you depends on what you order and how handy you are. The standard CJ harness comes in three main sections - engine bay, rear and instrument panel. There are some other parts such as the gearbox harness that are minor in comparison. iF your new harness is splt in the same way you can tackle it in the sections. Allow 3 to 4 clear days but a day beforehand to practice your wiring skills on some old bits.
If the harness you order is OEM spec and has the same connectors I would be surprised. You may find that even though buy one with connectors that some of them don't fit the equipment fitted to YOUR Jeep, hence you may well need to swap over an old connector. It is possible to reuse the old connectors if they are in good shape and you have the special tool to release the terminals from the back and a supply of replacement terminals. Jeephammer had a post called "Wiring 101" that exlained it all quite well.
Will it come with a new fuse box? If so what is connected to the plugs on the front of the old one? There are plugs on the front to plug in a stereo etc. and the PO may well have hacked in some other "improvements". How will you connect these other circuits to the fuse box? Have you considered a small ancillary fuse box?
What harness protection are you going to have? AMC fitted fusible links in two places on the harness to avoid the harness melting down in a short circuit. Are you going to use fusible links or MAXI fuses?
If you have non standard instruments or a stereo or CB you may struggle on the instrument panel, planning beforehand will be necessary.
You also have a fibreglass tub so you will need to install a ground system. the OEM harness assumes there is steel under many of the fittings. For instance the indicator lamp holders ground to the bodywork as does the instrument cluster. This grounding system will not come with the harness but is not difficult to make yourself, you just need a few drums of black wire and terminals with the wire being the same size or larger than the power cable going to the fitting. You can link it all back to a common point and then the battery negative, do not use the frame as it is a poor conductor compared to copper wire. You can buy some very sexy marine grade grounding bars or just connect everything to a brass bolt.
Dont forget the ancillary stuff, such as cable clips, cable ties, insulation tape, dielectric grease, heat shrink, sleeving and even cable markers. You will also need some specialist tools, proper connection crimpers, a good soldering iron, the tool that frees the connectors etc. Colour specifc wiring diagrams that show YOUR build would be very useful, laminated in A3 size is my preference.
It is worth doing properly, Puthijeep was rewired to a high standard by a PO, a lady in Government who was awash with bribes. The headlights work properly and nothing ever fails or falls off electrically. Bagusjeep was butchered by the Indonesian military and "improved" but things either do not work or work dimly.
There are plenty of threads on here from others who have done the same. Keith460 will have done it and his builds are impeccable.
BagusJeep lives in Bali.
1981 CJ7 258ci - Bagusjeep
1984 CJ7 258ci - Puthijeep
1981 J20 258ci - Gladys
1951 Willys CJ3A/MB/M38 - Little Willy
1995 Cherokee 4.0 - CHEROKEE