I cannot get behind the Gaydar postings. There was nothing sexual about his behavior - - that we know so far.
He said he was the Joker; consider that behavior. Loner. Mad at society and has no respect for the lives of feelings of others. Causes suffering without remorse; people are reduced to objects.
His booby trapped apartment fits into the Joker’s behavior well. It reminds me of the scene where the Joker meets with all the crime bosses and then shows the grenades he had inside his coat.
He became his own version of the Joker.
Look at the pictures when he was much younger and had brown hair....YOUR Gaydar will be going off.