The Dharma shastras have not mentioned anything about this matter. It appears that our elders also collectively have not suggested a solution for this. So, one could consider the place that they are in at that time; some do so. This is an opinion of adiyen alone.
Even within India, eclipses do not occur at all places; at times, there are significant variations in the timings of sunrise and sunset. During such instances, people follow what applies to the places they are at for rituals. Notably, last year Sankranti occurred over different days at many places in India. Some places followed the first-day occurrence and some other places followed the second-day occurrence. It appears that one can follow the details that are pertinent to the places one is at.