I must offer a somewhat different answer. I will add that I agree with other answers that it is atypical, but we don’t know your relationship with your advisor or their family. This said, the following is going to assume you haven’t met their father. I disagree that you should absolutely avoid doing this and therefore must present that POV.
Depending on how you approach the matter, you may visit the loved one of someone that has been so influential on your life, such as an advisor.
If doing so, I would:
- first stage the reason for your visit; talk about your background and the customs of your country:
“I understand this may be atypical in the [US?]; however, in my country it isn’t uncommon and considered a good gesture to... [visit members of coworkers and employers out of respect?]”
- I would also add some sentiment or attachment to legacy or indirect impact the person you’re visiting has had on your life, that might raise their spirits:
“I wanted to let you know how much your [son?] has impacted my life as my advisor. I know you mean a lot to [him] and without his help and guidance, I might be lost. His continued support and tolerance is a debt I may never be able to repay. I thought you should know the impact your [son] has had on my life.”
Now, I wouldn’t just show up out of the blue. I might also run the customs of your country by your advisor. First express your case and get their approval and ask for when a good time to visit may be. If you do visit, keep it short and sweet. People generally in an uncomfortable position don’t like like talking with people they don’t know.
One other note: although the common culture in developed countries does not do this, that does not mean that they didn’t in the past. The older generation sometimes have a better understanding of these customs and often welcome these gestures. To them, their life has passed by and they’re biding their time. They tell their stories to strangers on a park bench and they come from a time where boys swam together naked in gym class and guys openly changed in locker rooms - perhaps two weird examples for me to present, but they are striking difference that demonstrate how sensitivities have intensified in modern culture and just because “we” think something is indecent, does not mean it is to the subject.
Good luck with your decision. It is ultimately your decision and you must weigh your mind and your heart, which you’re doing a good job already simply by asking the question here.