Water – Does a water heater have to be completely full for the water to heat

The wait time to get hot water from a tankless heater is very common, especially when installed some distance from the faucet. The specs for different heaters varies as far as the volume needed to trigger to on. Most do not require full flow volume to turn on.

There are a few small point of use tank heaters, such as American Water Heater Company's Titan series (Lowes) that only store 2.5 gals of water and operate on 120VAC. You should have a separate 120 volt circuit for this type of heater however.

Keep in mind, 2.5 gals is a lot of water in one use, unless you tend to run hot water for longer periods of time. Your main tankless will deliver hot water to the small tank heater by the time temps drop in the small tank, theoretically the small heater will not need to turn on and the hot water will simply pass through.

What type of faucet do you have? If you have a pull-out faucet then you can detach the pull-out head from the hose (that reaches down under the sink) and see if the water pressure is good at that point. There are small parts in the pull-out faucet that also could have caught some debris (although cleaning them out may be a challenge). But at least you could have narrowed down where the problem is; i.e. is it in the pull-out faucet head.