If you like that exact switch, there are part numbers on the first switch that will let you find an identical replacement; I can't read them all in the image, but if you can read them and type them in, Farnell, Mouser Digikey, etc can find them for you (in their chat if you don't see them in a quick search on their sites). I'll try to do it myself when I'm more awake (I keep dozing off) if you don't find what you need before then based on the info here.
The technical term for that type of switch is a rocker, SPDT-center-off, latching. That means the actuator on the front rocks back and forth, and there is only one pole, or electrical path (in this case the center pin is common), and two throws, or positions, that connect the center pin to one or the other of the two outer pins, and the center position is off, not connected to either one.
So a physically identical switch with just on/off would be a rocker, SPST, latching. Only one pair of contacts, which is either connected or not. The voltage across the contacts shouldn't be a problem if the current is always low, but with a coil there can be a large inductive voltage spike, so making sure there is a diode wired in parallel with the coil, at the coil contact pins, will help minimize this. (the diode is always wired reverse-bias, so that under normal voltage it does not conduct, otherwise it would short out the supply voltage. Generally this means the bar/line end of the diode goes to the positive wire of the coil.).
I can't see p/n's on the second switch, but they might be there. If not, that pic and any numbers you can give them would let those sites find one that does the same job the same way.
For the operating method you describe, they would be pushbutton, SPST, momentary. (SPST for a single pair of contacts, if you need more than one set of contacts, to simultaneously operate multiple things, you can get DPST, or even 3PST, etc).
They are both standard switch formats, so there are waterproof caps you can get for them from the same places. Or even get switches that are inherently waterproof, though those are likely to be more expensive. YOu can get some spare caps in case they are damaged or wear out, so you don't have to replace the switches instead..
This is a generic image search for such caps, most of which are not the results you need, so I've linked some that may be the right type (but I would ask at the place you get the switches from to get you matching caps to ensure they will fit and work...if they dont' fit right, they won't keep water out).
https://www.google.com/search?&q=waterproof+switch+caps&tbm=isch
This probably doesn't fit your exact pushbutton switch, but is an example of the type (found with the google image search above)
https://www.newark.com/knitter-switch/et207/sealing-cap-waterproof-grey/dp/94M7264
This is not the same switch, just generally a pushbutton type, but the pics they have are better at showing the thread-on nut inside the cap that holds it to the switch and keeps water out of the switch.
https://www.ncsawparts.com/page/subpage/biro-sir-steak-pro-9-hd-parts/BIRO-SIR-STEAK-PRO-9-SWITCH-CAP-Ref-T3200A-T3105.htm
For your usage, you'd want clear silicone caps for the rockers so you can see the markings on them. The caps must have enough of a lip on them that goes securely under the lip of the switch at the panel mount to ensure water can't get under them and either into the panel or the switch.
This is an example page for the rocker switch caps to show what they should look like; they have a pretty good pic showing the lip.
https://www.ebay.com/itm/311659799585
