Let’s look at important things here –
Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.
Mrigshira - Mrigshira is nakshatra of desire oriented people. Someone who is keep searching for his next desire satisfaction. It is a nakshatra of disguise too. It is also related with Spying or Stalking and travelling. Please read this to get detailed info about Mrigshira - https://www.astrosaxena.com/mrig.
Taurus - As Mrigshira is part of Taurus, Taurus sign and its representations become important here. Taurus is the 2nd sign of zodiac belt, so it represents many things related with 2nd house of horoscope like, Hoarded Wealth, Assets, Savings, Finances, Luxuries and Liquid Money. All in all a sign related with luxuries and all the conveniences of life. Taurus is consisted of 2 and half Nakshatras, i.e. Krittika, Rohini and Mrigshira. Taurus' lord is Venus.
Gemini - As Mrigshira is also a part of Gemini, Gemini sign and its representations become important here. 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.
Venus – As Venus rules Taurus, Venus’ position and dignity is important to know about the overall functioning of any planet in Mrigshira/Taurus.
Mercury - As Mercury rules Gemini, Mercury’s position and dignity is important to know about the overall functioning of any planet in Mrigshira/Gemini.
Mars - As Mrigshira is ruled by Mars, Mars's position and dignity will also have an important role in functioning and results of any planet in Mrigshira.
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 Moon in Mrigshira Nakshatra – Now, when Moon is in Mrigshira Nakshatra, up to Taurus section of Mrigshira it is still in exaltation sign and as Mrigshira lord Mars is friendly to Moon, we can consider it as strong Moon. As Mrigshira is about searching, it shows a very research oriented mind. We can also say that it is mind which is always looking to accomplish its desires by outer means. So, it can also be termed as a materialistic mind. This desire of materialistic pursuit can be high in Taurus section as it is sign of wealth and assets. Real problem with this Moon comes when we reach Gemini section. Here Moon is in enemy sign. So, it gives a fickle mind which can't stay at one thought or one desire. It is always moving around for next object of happiness. There is a benefit with Taurus section that as it is an Earth Sign, person can still stabilize mind over one desire but when it comes to Air Sign Gemini, mind is just flying around. Other traits of Moon in Mrigshira can be research oriented, curious mind and at times they can have nature of spying or stalking too. Because of mythological story involved, this can be a sexual mind too. In Gemini section, they can be business minded too.
Role of Venus – Venus's position will become important in functioning and results of Moon in Mrigshira/Taurus as Venus rules Taurus. If Venus is in good dignity then Moon will have proper direction.
Role of Mercury – Mercury's position will become important in functioning and results of Sun in Mrigshira/Gemini as Mercury rules Gemini. If Mercury is in good dignity then Moon will have proper direction.
Role of Mars - Likewise, Mars's placement and dignity is important to guide Moon in right direction.
Other Factors – And of course, we need to consider conjunction, aspects, house lordship, house position and dashas etc to know the exact results of Moon in Mrigshira. So, we always need to take a holistic view of chart rather than just 1 planetary position.
Conclusion – So, this is how I see Moon in Mrigshira can work in a chart.