# Hausman test include or exclude time invariant variables? Favoring a random or a fixed effect model?

I analyse purchase decisions on different products j over a duration of t days. I would like to include random or fixed effects. When I run a Hausman test and include only the time variant variables, then random effects are favored rejecting fixed effects by prob>chi2 =0.075. When I include my time invariant variables such as product category (which is constant over panel=product j), then prob>chi2= 0.000. I am now wondering whether to use random or fixed effects. I thought it makes more sense to include only the time variant variables as usually the invariant variables should be excluded by Stata. I appreciate any recommendations.