Water – Wire size for water heater

I am going to try to brake down your question.

I have a 60 amp max tankless water heater.

Now just off of what you said the 2014 NEC Table 310.15(B)(16) shows that a #6 or #4 wire is needed for 60 amps, depending on which wire you use.

The circuit breaker is 60 amps.

You are right in line with the amps of the water-heater.

The water heater is connected to a NEMA 10-50 power receptacle

That receptacle is only rated up to 50amp but try to find a 60amp 3wire receptacle.

There a switch to turn on and off the water heater from inside the house. I am going to replace the switch. I noticed that it is a double pole 30 amp switch.

BIG problem, the switch is way under sized, but from your picture it doesn't look like the correct size wire ether.

I would look at the wiring that is going to the breaker and see if it is correct. You may have to start over again.

Interesting. In Canada the cable you need exists (2 conductor 12 or 10 AWG, red and black jackets, with bare ground), is commonly used to wire baseboard heaters at 240V and 20A, and can be found at any HomeDepot. The cable is even made in USA! See here for 12 AWG: https://www.homedepot.ca/en/home/p.electrical-cable--copper-electrical-wire-gauge-122---romex-simpull-nmd90-122-red---10m.1000108220.html; and here for 10AWG:https://www.homedepot.ca/en/home/p.electrical-cable--copper-electrical-wire-gauge-102---romex-simpull-nmd90-102-red---75m.1000108211.html

If you can't find it in the USA, then see Harper's taping solution in another answer.