A Jew must not only refrain from forbidden activity on Shabbat and Yom Tov, but also may not receive direct pay for permitted work he performs on those days. The commercialization of permitted activities causes them to be included in the prohibition of commerce on these days.[1] One may not receive payment even for renting out utensils for Shabbat, even if no Jew uses them for any type of work.[2]
It is possible to circumvent the prohibition in most cases. If the pay relates not only to Shabbat or Yom Tov but also includes work or rental during the week, then the problematic payment is “swallowed up” in the permitted payment.[3] There is much to say about when a payment is deemed directly linked to Shabbat and when not, but we will see that there is no need to elaborate further in this case.
In truth, one is not really paid for vacation days. Rather, one is paid for the work that he does during the period of a year (usually), with the payment dispersed throughout. The employer realizes that his workers need time off for recreation, family needs, and religious and/or civil observances. He thus pays his employee for a year’s work, taking into account that out of 365 days, he allows him not to work on vacation days. Thus, in reality, you are simply not being penalized for the day off, whether it is the civil New Year, the Jewish New Year, or Yom Kippur. Even if you did get paid extra for Yom Kippur falling on Shabbat, it would be because of an additional benefit that some employers give. The rationale is that one who has less leisure time than he “deserves” is compensated for his expanded work schedule by an increased salary. You are not being paid for doing something on Yom Kippur, and there is no halachic problem to receive payment. There would be a serious question if a Jewish worker asked his Jewish employer to pay him overtime for work he did on Yom Kippur. That sensitive issue is not included in the question you raised.
However, the following consideration is crucial to keep in mind. (Because several items are unclear in your question, we respond provisionally.) Not only are you not being docked pay for Rosh Hashana and Yom Kippur, but these days are not even deducted from your general vacation time. You are not even being asked to come in on gentile or civil holidays to make up for your extra absences. This is a generous arrangement, which not all observant Jews are awarded. Thus, it seems highly inappropriate to attempt to turn this special privilege, which is intended not to interfere with your religious observances, into an opportunity to make extra money or get extra days off that others cannot. Please realize that less than 100 years ago, Jewish employees were forced, sometimes sadistically, to choose between keeping Shabbat and Jewish holidays and being fired. We should be thankful that many elements of society are as accommodating to us as they are, especially in your case. If our understanding of your situation is correct, then it is wrong and likely a desecration of HaShem’s Name and a debasement of our people’s character to try to enforce the wording of the contract[4] to take advantage of your employers’ good will.