Timing the funding of Roth IRA

Our Roth IRA money is invested in two vanguard mutual funds (one international and another large cap). Its about two years since we started roth IRA accounts with vanguard. Over this period i have noticed that the time of the year when mutual fund is funded matters. Personally, i feel funding mutual funds between December mid (after mutual fund pays the dividend) to Jan mid would be the best. The market in general seems to be down around Christmas eve (tax loss selling?) and also most mutual funds pay the dividend before christmas eve is paid. These two factors seems to lower the value of the fund during that period, allowing you to invest during the lowest point inf value to gain the best appreciation of your money.

There seems to be two pointers against this thinking
1. While timing the funding of mutual fund is not exactly timing the market, the value of the fund is closely tied to the market. So if you take a long term view (more than a decade view), the time of the year when you fund the mutual fund should not matter at all.

2. Since this is a roth IRA, dodging the mutual fund distribution cycle should not matter