Tastytrade does not give a whole lot of attention to technical analysis (aside from Slim and a couple of the other guys). The reason is that they come from the fair market school of thought. They assume that in an efficient market everything that can be know about a stock is already priced into it. When new information becomes available it quickly is priced into the stock. As far as they are concerned as long as a stock is trading efficiently and is liquid the movement either way is basically a 50/50 shot. They are contrarian traders and therefore will go long when they believe something is weak and go short on something they think is too strong. They do scalp on the side but the bulk of their philosophy is wrapped around selling premium (theta (time decay) and volatility). They do allow that technical analysis has it's place but mostly just as a tool to give someone a direction to choose. They believe that you can use whatever you want to pick a direction but it is the option strategies themselves that give you the edge.
Tom and Tony have been trading since the 70's or early 80's and started out as market makers on the CBOE floor. Tom developed Thinkorswim, Tastytrade and Dough.com.