However in the five books of Nachman we do not find any specific connection between Rosh HaShanah and his grave site. He never took two two witnesses saying to come to his grave on Rosh HaShanah like he did for the Tikun Haklali (note 1).
If Reb Nachman had said anything that would have indicated that he wanted people to come to his grave site on Rosh HaShanah do you think that Reb Nathan would have omitted it?(note 2) We know Nachman from Breslov wanted people to come to his grave to say the Ten Psalms because he took two reliable witnesses [neither of whom was Reb Natan] and declared this in front of them. And said specially that he would do everything to help that person. But he never took two witnesses about Rosh Hashana nor even said a simple statement like, "Come to my grave on Rosh Hashanah."
When he wanted people to come to his grave he said so openly. When he wanted people to come to him, while he was alive, on Rosh Hashanah, he also said so openly. But he never said or implied to come to his grave on Rosh Hashanah. And in fact no one, including Reb Nathan, came to his grave on Rosh Hashanah. They came to Uman, but not to his grave.
When he wanted to discuss his grave he did so in many ways. But his grave was never mentioned in the context of Rosh Hashanah.
[The obvious question then is: why did he not take again two witnesses and testify before them concerning some connection between Rosh Hashanah and coming to his grave? In theory he could have one so. And why was Reb Nathan not one of the two witnesses?] This does not mean that it is not a good idea to go to Uman for Rosh Hashanah. But there is no mitzvah in saying that Reb Nachman specifically said to do so. He certainly did not. Appendix:
(note 1) 16,32, 41,42, 59, 77, 90, 105, 137, 150 (Russians have a different way of numbering the psalms because they consider nine and ten to be the same psalm. So to them the numbers are different.)
(note 2) Reb Nathan did in fact begin the coming to Uman on the very first Rosh Hashana after Reb Nachman had passed away. So it seems clear that Reb Nathan understood this to be a good thing though not explicitly stated as such by Reb Nachman. However the saying of the ten psalms by his grave site was in fact explicit.