Aloha Bill,
If you are talking about a wiriung harness prefabricated for a TR3 it should go fairly quickly, perhaps in less time than you figured. Things that may slow you down are the dash board instruments because of the small space to work in. Lossening the center instrument panel so it can be pulled forward out of the dashboard will make it easier in my opinion. Becareful not to break the capillary tube to the temerature gauge. You may need to scavange some wires from the old harness for instrument lighting and ground wires. Also most new harnesses do not include head lamp and front turn signal sub harnesses.
The harnesses I bought from either Moss Motors or British Wiring had most of the wire ends fitted with the appropriate connectors. If you need to install all of them it will certainly add several hours to the job.
Remember, the TR3 doesn't have relays and feed back loops to indicate burnt out bulbs. It is a simple car electrically, wires go from power supply to the bulb and sometimes there is a ground wire. It can be done in a weekend or perhaps even a day. I found out as I got older it takes a little longer to do than it used to.