I need to clarify some of the info that has been presented up thread as there is some conflation. Note: I did not watch the link provided by @psneeld #15.
When specifying a conductor to use in an electrical circuit aboard a boat where the ABYC Standards are used, there are two physical properties to consider; conductor ampacity and voltage drop. For AC circuits only ampacity need be considered whereas for DC circuits both ampacity and voltage drop need to be considered. My experience has shown that if a DC circuit is sized properly for voltage drop, then ampacity requirements will be generally met.
From a practical point of view, ampacity is the ability of a conductor to carry current without melting the insulation (or the copper, for that matter.). "Boat Cable", an actual UL designation (UL1426) is most commonly used in the USA (Ancor, Corbra, Pacer, etc.) has insulation rated at 105C dry/75C wet. Look at a piece of Boat Cable and you will see this marking every foot along the conductor. BTW, Boat Cable is not required to be tinned.
Ampacity is also affected by the ambient temperature of the conductor's environment and any bundling with other current carrying conductors.
The ABYC Standards have two environmental temperatures to consider on a boat: in a machinery space (50C) and every place else (30C). The ampacity of a Boat Cable is derated if it is used inside a machinery space. Similarly, the ampacity of a Boat Cable is derated if it is bundled. The ABYC Ampacity Tables provide for these conditions.
Voltage drop is a function of conductor composition (always copper for Boat Cable) and circuit length. For DC systems, ABYC specifies a maximum voltage drop of 3% for critical loads (bilge blowers, navigational lights, etc.) and 10% for everything else. At the lengths of vessels commonly discussed on Trawler Forum, circuit length is not a factor for AC circuits.
So, back to the OP regarding sizing the conductor: Assuming a single 1200W heating element; the maximum current would be I = P/V > 1200W/120V = 10AAC.
From ABYC E-11, Table 6C (and other sources): 16AWG Boat Cable bundled with up to 6 current carrying conductors has an ampacity of 12.8AAC in the Engine Room. Personally I would use AWG14 Boat Cable with an ampacity of 17.9AAC in the E/R.
I have no opinion on the switch. For the OP, IYB (It's Your Boat).
Hope this helps.