Questions about hot water tank and furnace

First of all with the hot water. There is a bypass valve that may have been shut when or if the TT was winterized. Check that most are under the sink.

The thermostats in most RV's are small. Look carefully at the dial/levers if yours is not computer screen.

Lever has to be in heat or A/C position for them to work.

There is ALSO a lever for "fan only".
That means no matter if the heat lever or A/C lever is on it will ONLY just blow fresh air. You need to make sure the fan only is in the off position.

Lastly there are delays on both A/C and Heat. You start flipping back and forth and on and off on those switches and the delay kicks in and heat or cool will not come on.

Delay Should only be for 3 minutes or so but if feels like forever and your brain immediately goes into 'oh no the furnace or A/C is broke'.

Furnace is usually under the stove. Position of furnace varies from RV to RV though.

Hot water heater and access to drain is behind a door on the side of your RV. That position varies also.
Hot water heater is behind a door on the side with a grate/screen also.

Welcome to the forum. The hot water tank is "built into" the water heater. If by "flipping the switch near the sink" you mean out the WH on AC power, you will have to check for power at the WH itself using a test meter. The power goes to a thermostat located on the outside of the tank then to the heating element inside the tank. Here's a link to a parts breakdown and illustrations.
As for your furnace, walk around the outside and see if there are two openings located close to each other on a metal plate. That's your furnace's location. If yo8u don't find the combustion intake/exhaust, your heat will be electric only and be provided by the rooftop unit.

Others will be along,
Teach

Most common position for a not water tank to be located is central to all users of hot water. This often puts it under a kitchen or bathroom cabinet and often you have to remove screws from opening to access it. If if works, it's likely bypassed for winter so no water getting into it. DO NOT turn on electric switch unless you know for certain it has water in the tank. It takes almost no time at all to burn up the electric unit when turned on with an empty tank. Find the inside access to the water heater by finding the OUTSIDE service pannel and going to the same location inside the trailer. Get that service panel open and check the bypass valves. If necessary slightly lift the pop off valve to see if there is water in the tank.

The furnace is located under a counter, seat etc. in most cases. You should be able to see the cold air return grate on a wall, side of the dinette of on a cabinet wall. That will locate your furnace. The grate would likely be 12" by 12" or a little larger in size for a trailer your size.

Good luck / Skip

Spend some time on your hands and knees while searching for your appliance locations and copying down the brand and model number. Use your favorite search engine such as Google and type in the brand, model number, and the word 'manual'. Most all manuals are available online.

Can't help on the heater issue, my systems are totally separate. The wall thermostat controls the furnace, the air conditioner is controlled manually on the ceiling unit itself.

On the water heater, it's all one unit. Look outside and find the access panel for the water heater. The tank is right there behind it.

Does the water heater work on gas? I know on my trailer the wall mounted switch is for 110v usage only, so obviously you need to be plugged in for the electric heater to work. In addition, there is a dedicated breaker in the trailer's sub panel just for the water heater. I keep this off all the time since I don't want it accidentally turned on when I'm plugged in at home. Maybe the previous owner kept this breaker off also? Check your panel and see if there's a breaker for the water heater.

If you are trying to get hot water from electric (shore power) it takes a loooong time to heat. Yours being a little older, I am not familiar, but either outside behind the screen, or a switch on the panel that tells you tank levels should be a switch to run on gas. MAKE SURE YOU HAVE WATER IN TANK. To do this, connect water hose to to your city water connection (make sure you use a pressure regulator) open the screen cover for water heater an open relief valve till water comes out. If no water, find the bypass valve

If you have not done so, turn on the gas and light a burner on stovetop to bleed air from the gas lines

Regarding the WH
In addition to the wall switch and breaker
My camper has a service switch in the outside WH access door compartment

If someone has turned that switch off then the electric element can't get power to operate

Might want to check that out

Thanks to everyone for all the great responses! Your help is greatly appreciated!! Mysteries solved. The hot water tank was hidden under the head of the bed. Little did we know there was an access door there as well as storage at the foot of the bed. And the furnace was exactly where the previous owner told us the fridge access was (guess he never opened it).