to search for, to look after
覔 centers on actively seeking or looking for something, with an emphasis on visual searching. The sense of looking after someone or something extends naturally from the idea of keeping a watchful eye.
覔 is a variant form of 覓, combining 不 (not) with 見 (see) to express the idea of searching for something not yet seen. The exact historical development is uncertain, but the component relationship is clear.
The top 不 suggests something missing or not present, and the bottom 見 means to see. Imagine scanning a room with your eyes, trying to spot what is not yet visible—that is searching.
For ベキ, picture a detective searching for a clue, saying 'I must find the key!' The word 'key' sounds like ベキ, and the detective is actively looking for it.