In my story I have an enigmatic order putting pressure on the financial backers of the archaeological expedition that my main characters are on, I'm just not sure who usually backs archaeological expeditions and I want it to be as realistic as possible.
Some museums. For example, the Field Museum in Chicago has funded many archeology expiditions. It could also be funded privately, like by a millionaire or private company with interests in archeology.
Nearly 90% of archaeology is Cultural Resource Management archaeology. It is funded by companies who are looking to build on land. Before construction most states require archaeology to survey and see if there is any culturally sensitive material, if so they must excavate within a small span of time and remove any and everything worth information. This is how the field of archaeology keeps functioning. The other 10% is funded by universities or schools for research and learning purposes. Museums rarely fund expeditions anymore, and the legalities of private funding has been brought into question. Private investors that give funding in order to add to their own collections are in fact breaking the law. I am actually an archaeologist, in case you were wondering were my info comes from. Hope that helps.
I don't where they usually get their funds from but extremely rich people often give funds to anything they are interested in. A group of rich guys could give quite a big amount of funds to something if they all are willing to.
also historical societies... and possibly governmental agencies in that country, if the site has historical national importance...
Don't forget organizations of particular cultures. Although some will oppose the excavation of sites, particularly if burial sites are present, others may wish to recover and preserve tangible pieces of their heritage. This can be particularly true if there are factions who disagree about part of their history, and may wish to find the proof they believe can be found at a particular location.
yes, those too... and don't forget national geographic-funded expeditions, some of which have made great discoveries...