Google is an unreliable resource for finding images because many museums do not have fully digitized collections (images and databases). The tl;dr reason for this is because building a database and photographing high resolution images is an extremely expensive and time consuming process. What you will be able to find through a search engine is also limited if you cannot search in Hangul. For example, here is a video of an imperial portrait hall which appears to date to the Joseon period.

For your purposes, I think that you would be better off looking for portraits at a specific website, such as the National Museum of Korea (note that many of these portraits are of meritorious government and scholar officials, which should be sufficient indication that there was a strong portraiture tradition in historical Korea. These in particular are tied to moral conduct). This book, published in 2007, also seems to contain a selection of royal portraits from the Joseon Dynasty. Unfortunately, I am not able read Korean or find an electronic copy of the book, otherwise I would supply you with the images. The National Palace Museum of Korea is also a good resource, but again, images are limited. The linked page seems to have a VR tour, so you should be able to get a view of some of the portraits they have on permanent display. If you go through past exhibitions and the collection highlights, you can see different kinds of representations (e.g. commemoration of Prince Hyomyeong's matriculation).

The bigger picture question you seem to be pointing at is the historical tradition of portraiture in Korea, and what circumstances someone would find it appropriate to engage in self-representation (or commissioned representation) that privileges verisimilitude (i.e. showing what the person looks like). This is a big question that I am not qualified to answer. However, there is an upcoming exhibition at the Asian Art Museum in SF on this very subject. You can get a peek at some of the works that will be on display here. I am uncertain if there will be a museum catalogue, but am hoping they will produce some digital materials to supplement the show.