I'm going to bet that omission will look completely odd. If this is going to cause a gap of a month or more, than it will look weird to omit the experience entirely. I'm leaping to the conclusion that this was your full time job and you spent a non-trivial amount of time in this role.
If, however, you supported a legacy system for a few hours a week and you had a way more interesting other job, feel free to omit.
Absolutely. It's part of your job history.
- if you want to continue to use the legacy technology, highlight all the jargon on your resume.
- if not focus on the softer side - the area of responsibility, ingenuity, and big picture perspective and independent problem solving prowess.
If you are focused on keeping up with the legacy technology, then emphasize that.
If not, you want to set the tone of dedicated but willing to learn. Be actively engaged in learning something new and make sure it's on there. I hired an awesome last man standing who had never worked in my subject domain, but who was going to school nights to catch up and working on a personal project in my domain. It showed he was willing to take the initiative to learn and didn't expect it to be easy.
An answer to the question "why are you looking?". It should be more than "there is no job available in my current company". It may be true, but be clear on why.
These answers sound good:
- My company is moving all work like this to another location and I'm not willing to move.
- My company is dying and now that the product is loved is gone, so am I.
- Everyone I liked and respected left.
- The only options in the local location are an unacceptable work/life tradeoff.
- I don't see very interesting work in the company. I like X, they do Y.
These answers don't:
- I have no idea, but my boss told me to look.
- All the jobs in my company turned me down.
- I hate new technology and I don't want to learn it.
Most companies that aren't doing a radical move want to retain good people who work hard - so the goal is to present the fact that the company is making a radical move, rather than that you aren't a great person that the company would want to retain.