It is true spending a month there is showing interest, but the program is looking for more than just the volunteering of 1 month of your time. They want to see someone who is a good fit for their program. You'll hear that 'good fit' statement alot, but what does it mean? I'll try to explain it.
First they want to avoid someone with red flags, and believe me those who go into medicine often are eccentric or odd lol. They want to see if you have good social skills, can talk with a patient and talk with other physicians/residents comfortably. This may sound simple but I've seen many medical students and residents in their weakest moment snap at patients, co-residents, shut down in front of attendings, fight with others, and just not handle the fact that they can be wrong. There is a surprising amount of people in medicine who have been 'right' all their life and have a VERY hard time finding humility day to day being told they are wrong and need to keep working on this or that. That is a big deterrent to being appealing and honestly what happens to alot of medical students who a sub-I didn't help. One time arguing with an attending, or snapping at a resident in a 31 day sub-I and that can tarnish your entire reputation. some people can't make do it.
Other things is ability to learn (kinda folds into what is above). if someone is arrogant, can't take criticism they will be very challenging to teach. also if someone is just clueless (there is a few medical students this falls into) and you can tell they don't learn as easily or quickly as their peers. but the latter is much more rare than the former. I'm talking 1% clueless vs 99% inability to take criticism.
finally enthusiasm each day. you want someone who can be down in the trenches with you in residency and bring positivity to the program while still upholding all the other expectations (learning, doing good work, etc). So if a medical student gets grumpy or burnt out doing 80 hours a week for 4 weeks, what will they be like doing 80 hours a week for 3-4 months in a row? this is a bit more intangible but it does make an impression.
those are the things I notice, It is certainly not comprehensive but in my mind if you can avoid those things then you would be considered a 'good fit' for most any program.