Where do I find the make and model number?
If the manual for your HVAC system is in the documents for your boat, you might find it there. Otherwise, you'll have to look on the equipment itself. If the HVAC system on your boat is like a 2012 R27, it is a "split system" where the compressor and air handler are in different places-- the compressor is under the footwell of the port companion seat and the air handler is in the cuddy.
Access to the compressor on 2012 R27s is gained two ways. 1) Remove the upholstered panel on the back port side of the cuddy. With that removed, there is an insulated panel that can be removed that provides limited access to the area under the port companion seat footwell where the compressor is located. There is a rectangular control box on top of the compressor that should have model and serial number information. 2) The other way to gain access to the compressor is to crawl to the forward end of the "cave"and remove the panel at the back end. Not an operation for the claustrophobic.
Access to the air handler is gained by removing the cuddy cushions. I'm pretty sure a fault in the reversing valve does not require access to the air handler.
If the model number is not in any of your boat's documents, before going to all the hassle of trying to get it off the equipment, call Dometic and tell them that you have a Dometic HVAC system installed in a 2010 Ranger Tug R25. There's a slight possibility that, if indeed a Dometic system was used in 2010 R25s, they will have records of what was installed on those boats.
I sure wish there was someone here on Tugnuts with the same model and year R25 that would know what was installed and reply. I'm just speculating that what was installed in your 2010 boat is the same as my 2012. Just understand that systems sometimes changed from model year to model year. For example, a 2016 R27 does not use the split system used on the 2012.