The full ingredients lists for vaccines (I'm in Australia) are not easy to find and Covid vaccine ingredients have only been made available more recently, but they're still not easy to find for all vaccines by googling. There are also variations in ingredients and amounts between the pharmaceutical companies.

There are no indications on any of the lists I've found to say which ingredients are most likely to cause an unintended reaction in some people. That requires another lengthy googlesearch for each and every ingredient mentioned.