@Adnan just wrote an excellent post in the Ten Hag thread, that goes into why a fullback that can 'invert in-field and play in midfield' is crucial to enabling the midfield part of the build-up/attacking style Ten Hag will want to implement - see the bolded bits below. In that sense, getting the right RB signing might be a higher priority than people think: it's not just about adding an attacking thread on the right that better complements Antony's particular style/skillset.
I suppose this doesn't necessarily change the priority list (CF ahead of GK/CM ahead of RB), but I'm thinking it might rank the RB priority a lot closer to the others than people seem to think. That might mean, for example, that it's more important to Ten Hag to sign exactly the right RB if he's available now than to sign a CM or GK stopgap that still doesn't really offer what Ten Hag needs.
I don't know if that 'exactly the right RB' is Frimpong, mind. Could he play this midfield role, or is he 'just' the type that flies up and down the field along the touchline? (@Zehner, @ForEverEleven? I would think Dumfries is primarily like that and hence not really what Ten Hag would need.) I'm just trying to provide some further tactical context.
I wouldn't worry too much about that as long as you play him with a CM that holds his position. Frimpong is definitely more of a wide player but I wouldn't say he's not suited for the system @Adnan described. In the end, you build up in a 3-2-5 formation in possession and some sort of 4-4-2/4-3-3 against the ball. But how the players rotate between positions is different from team to team. For instance, although Cancelo and Frimpong would both play RB against the ball, Cancelo would be one of the two CMs in possession while Frimpong would occupy one of the 5 attacking positions.
For instance, Alonso rotates in the following ways. Base formation 4-2-3-1:
-----------------ST------------------
--LW---------AM---------RW---
-----------CM-----CM------------
--LB-----CB-----CB-----RB----
In possession, he switches to:
------------------ST--------------------
--LW------AM------RW-----RB---
-----------CM-------CM-------------
------LB------CB--------CB---------
Occasionally he even starts two attacking FBs and has one CM drop between the CBs:
-----------------ST---------------------
--LB----LW--------RW-----RB---
-------------CM-----AM-------------
------CB------CM------CB---------
In contrast, a team like City that has FBs who are very comfortable in the CM and CMs that like to attack, rather lines up like this:
----------------ST-------------------
--LW---AM-----CM----RW---
-----------LB----RB--------------
------CB----CM-----CB-------
There are almost indefinite variations and many coaches vary based on the players in their team, often from season to season, if I'm not mistaken. In the end, you need a set of players that complement each other well. What you don't want is e. g. Busquets and Rodri in CM and Cancelo and Trent as FBs since all four would like to play CM in possession.