Should I apply for 2 jobs at the same employer?

I need to find a job in the next few months. I'd been eyeing a particular part time position that would be really good for me, but I procrastinated a bit. When I got my resume and cover letter together, the job had disappeared from indeed and their website.

The same organization had a somewhat similar position still open, but with full time hours. I'm coming back into the workforce after 15+ years on disability, so I prefer part time at least to start. But the part time job was gone, so I reworked the cover letter and submitted it for the full time position.

This morning I checked and the part time position is back on both sites and says, "Hiring multiple candidates". These jobs have been open for over 6 motnhs, this is a hard area to hire in, especially given the wages.

The full-time position doesn't have any contact information listed, so there's nobody I can email and say, "Would you also consider me for (other position)?". It's not a large organization. I'd be surprised if the hiring manager was even a different person, but only the part time listing had contact information listed.

Should I just submit for the other position? Or wait and see if I get an interview/hired before applying for the other? I get the impression that they'd rather fill the full-time position, and it's a better fit for my resume/skills. I don't think it would look good to immediately apply for the part-time position after selling myself as the perfect person for the full time.

They haven't even had 1 business day to consider my first application. Indeed says they normally respond within 1 business day, but I don't know how trustworthy that is.

So, should I apply or wait a bit?