I don't know what are "Input Methods" but I don't think "Write Unicode BOM" should be in the context menu. If no one supports this request, I would be inclined to close it.
"Input Methods" are a special items present in context menus of inputs/textboxes/etc. that allow entering characters from another language when you don't have those keys on the keyboard (ex. typing Traditional Chinese on a US English keyboard) or special Unicode characters on any keyboard. In Linux I believe it's provided by IBus, and AFAIK it's supported natively by GTK+.
While I don't use this myself, it's probably good to enable it if supported by GTK+, for accessibility purposes.
Oh yes of course, I've already used this feature here and there. I thought it was a Mousepad-specific menu entry that would have disappeared since the time this issue was opened!
It is better to use the system-wide input method framework for changing input methods. Modern desktop shells offer on-screen displays for this that can triggered with a keyboard shortcut, e.g. Super-Space.
Frankly, I tried to see how I could use input methods as a user, and I had a bad time. The Arch Linux wiki didn't help me, it's totally abstruse. All I was able to do was to install Onboard to have a virtual keyboard.
Well, at least on our side, if I understand correctly, we shouldn't try to implement something at the application level, but rely on dedicated external tools (it's up to the user to find them, install them and make them work...)
So I'm closing this issue, it's been 7 years since anyone has been appointed to work on it anyway, so the probability of it changing is pretty low.