Technically, "he" is perfectly acceptable for gender neutral texts. Merriam-Webster states that "he" can be "used in a generic sense or when the sex of the person is unspecified".

However, to avoid the appearance of non-neutral text, I usually use "he/she", "his/her", etc. "They" or "their" can be used, but these are not really appropriate referring to a singular antecedent, so I quite often use "his/her" rather than "their". Another technique that you see frequently and that I sometimes use is to use "he" sometimes and "she" other times. As long as these more-less balance out in your text, you should be OK from a neutrality standpoint.

Any of these alternatives is preferable IMO to "ey" and "eir".