Open/close picker when input is focused/blurred

[billdami]

I'm looking to more closely mimic the behavior of the PIkaday picker (i.e. like the one in this demo: https://pikaday.com/) where the picker calendar will open when the input is focused by tabbing into the field, and the closed when the input field loses focus via tabbing away (while still maintaining the ability to open/close it via clicking the input/clicking elsewhere).

Is there a existing pattern for accomplishing this? Trying something like a simple onfocus={{dp.actions.open}} action on the input seems to conflict with the ability to close on selection, as the input regains focus after selecting.