I replaced my thermostat on my honda civic 160i

SOURCE: 96 honda civic lxi overheating.

The car is not overheating if the temp gauge goes up and down by turning the lights on and off.  The gauge is giving you bad information.   You can confirm this by starting the car from cold, sitting in the driveway, let the temp go to somewhere BEFORE normal operating temp, then turn on headlights and fan blower on high, watch the gauge, then turn them off.   If the gauge moves significantly from the electrical load, you probably have a short or a bad ground connection.  

You have a short circuit or bad wiring somewhere in the front half of the car.  I don't know what thermostat switch you have replaced ... but it's not the problem .. stop buying them.  
If you are the original owner, was there an accident that may have damaged some wiring?  If you bought the car second hand,  get a carfax and find out where the thing was hit ... concentrate your wiring trouble shooting in that area.

I think it is something OTHER than the temperature sending unit or the gauge

SOURCE: Temperature Gauge in 2000 Honda Civic LX

hi from uk from your symptoms of what happened re temp guage risen suddenly it would indicate the temp sender unit on the engine has blown ie is earthing to engine via its screwthreaded body this is just a matter of replacing with a new sender unit hope this helps

SOURCE: fuse diagram for 1996 honda civic

try this link... let me know if this is what you needed... http://img530.imageshack.us/img530/8770/9600civicfuse98civicexatb2.jpg

SOURCE: 2003 Honda Civic runs hot when idling.

Check the cooling fan switch. It appears your auxiliary electric cooling fan isn't going on when at idle. and engine temp increases. While you are driving, air is being rammed thru your radiator as you cruise along, so it isn't overheating, at idle, that isn't happening, and the fan should go on as the temp goes up. When the ac is switched on, the fan is being signaled to operate due to the heavy ac load on the cooling system.

SOURCE: '94 honda civic is overheating, temp gauge is

Yes it looks like it. Provided you installed the thermostat in the correct direction, Here's the test, remove the radiator cap, start the car and wait for the engine to warm up, When you can see the temp begin to rise on the gauge the thermostat will open. While reving the engine look for turbulance in the coolant/antifreeze in the radiator opening.
If none is observed then replace the water pump.