Empty value within data validation dropdown
I have managed to do this by adding a single quote <'> to a blank cell.
It works for me as shown here:
On selecting this it shows up as a blank line.
This doesn't seem possible. Empty strings are ignored if they are provided among the options; this happens both directly in a spreadsheet and when building validation rules from an array of strings via Apps Script. This is probably because validation rules are ignored when the cell is empty, so allowing an empty string would be redundant. Unfortunately, this also means you can't have an empty string in a in-cell dropdown.