Let’s look at important things here –
Mercury - Mercury represents communication skills, marketing, calculative ability, younger siblings, hobbies, skills with hands, intelligence, quick decision making, logical thinking, youthfulness etc.
Punarvasu - It is a nakshatra of rehabilitation and recovery process. It is very closely connected with after-care medical activities. It can also be a nakshatra of counselling. For more information on Punarvasu Nakshatra, please check this - https://www.astrosaxena.com/punnaksh.
Gemini - As Punarvasu is part of Gemini, Gemini sign and its representations become important when any planet is in Punarvasu/Gemini. Gemini is the 3rd sign of zodiac belt, so it represents many things related with 3rd house of horoscope like, Communication Skills (either written, oral or even by sign language), Marketing, Business etc. It is a sign basically related with communications and business ideas. Gemini is divided into 2 and half nakshatra of Mrigashira, Ardra and Punarvasu. Gemini's lord is Mercury, which is significator of Communications.
Cancer - As Punarvasu is also a part of Cancer, Cancer sign and its representations become important when any planet is in Punarvasu/Cancer. Cancer is 4th sign of Zodiac Belt, hence it represents the things represented by 4th house like Mother, Mother's Care, Emotions, Taking Care of Others and Nourishment etc. Cancer is consisted of 2 and half Nakshatras namely Punarvasu, Pushyami and Ashlesha. Cancer's lord is Moon, which again represents almost same things which Cancer and 4th house represents.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Punarvasu/Gemini.
Moon - As Moon rules Cancer, Moon's position and dignity is important to know about the overall functioning of any planet in Punarvasu/Cancer.
Jupiter - As Punarvasu is ruled by Jupiter, Jupiter's position and dignity will also have an important role in functioning and results of any planet in Punarvasu.
Houses Involved – Also, we can’t afford to forget the houses involved as a planet can be ruling different houses and sitting in different house for every person as per ascendant and planet’s position. To know overall affect, we have to consider the houses involved as those areas of life are being impacted.
Interpretation of Mercury in Punarvasu Nakshatra – Here, Mercury is in nakshatra of its enemy Jupiter but sign-wise, it will be in own sign in Gemini section and in enemy sign in Cancer portion. So, its a mixed dignity or strength for Mercury. Punarvasu, from name itself and then from mythology story too, is nakshatra of rehabilitation or recovery related work. Now, if we apply Mercury's traits to Punarvasu, it creates a person who can be in any business related to any kind of rehabilitation related work. In Gemini section, they can be in communication, teaching and counselling related business which helps people to rehabilitate or recover from their issues. In Cancer section, they can be directly working in health-care or medicine or teaching field by which they can help others to recover from various issues in life. Mercury in Gemini section is still better because in Cancer section, these people lose the right sense of judgment and they decide the matters of their own life on emotional base. For ex, if a person has cheated them and starts crying in front of them then a person with Mercury in Cancer can again trust that fraud. Overall, it is a great position to become healer, counsellor and teacher.
Role of Mercury – As we are trying to interpret Mercury only, we need not to look at Mercury's position separately.
Role of Moon – Moon's position will become important in functioning and results of Mercury in Punarvasu/Cancer as Moon rules Cancer. If Moon is in good dignity then Mars will have proper direction.
Role of Jupiter - Likewise, Jupiter's placement is important to guide Mercury in right direction, being Punarvasu's lord.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Mercury in Punarvasu. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Mercury in Punarvasu can work in a chart.
Hope this helps. Please post any comment or query you may have.