Disclaimer just my Personal experience.
I've some issues with my body so I can't really do something as well as I envision them at least for now.
My advice would be to enjoy it. When I "enjoy" often I close my eyes I think it makes it easier for me to focus on proprioceptive information and the feel of water.
Clearly you can't do it all the time, especially in the beginning (not going straight), you don't have to do it on the whole stroke cycle but I think it helps getting the "sense" of this new medium.
In the water you are not blind but I believe that a lot of ours sensitive references are off and more need to be developped (skin/tact for example).
If you can do video of yourself one way or another, I did not and I think it would have save me time as I would have realized glaring issue much earlier.
I stillI don't use chronometer for some personal reason biut it is needed as the feel of water and "sense of speed" may be missleading.