The BT-99 (new model or old) does not have a drop-out trigger assembly like some other guns do. So, you really can't just "take out" the "trigger". For the BT-99 (like many other break-open guns), you must remove the stock to gain access to all the internal parts (hammer, mainspring, sear, trigger, etc) . . . then start removing these parts from the receiver, which usually involves driving out pins, working with strong springs under compression, and likely some re-assembly quirks.
In summary, you don't really need to be taking it all apart just to clean it. Simply remove the stock and clean the inside of the receiver while everything is still in place. Disassemble the internal parts only if something is broken, worn, or otherwise needs replacement.
My Older B T 99 was bought at Jacquas in Findlay OH for a retirement present for myself in 1998
She is my baby. I have several newer trap guns but this gun will always be my favorite s I needed to learn how to clean the trigger assembly. My friend that did it for me all these years is no longer able to do this. Thanks for your help