In my experience, churches which offer the TLM or are exclusively TLM do offer confession more often. An example is last year when I was traveling to Kansas City and needed to go to confession. The diocesan cathedral, which presumably has several priests available, had confession twice a week for about an hour, neither if which time I was able to make. The local ICK church offered confession every day at a set time, and 30 minutes before every mass. I have had similar experiences in other places.
There are some NO-only parishes that do offer abundant confession opportunities. Some offer very few. You get both extremes. But I think a TLM parish is almost guaranteed to have frequent, if not daily confession. At least, I have yet to discover one that does not.