When you come across a product, you can quickly try to add it to your inventory, and Amazon will tell you if you are gated or not. So, it may say "You need to request approval for the category Beauty and personal Care", at which point you will now know you are gated in that category. 


Here is a link which goes over some categories as well from seller central: https://sellercentral.amazon.com/gp/help/help.html/?itemID=200333160&ref_=xx_200333160_a_r1_cont_sgsearch




What categories am I gated in as a new seller?