I started some changes I will undo

scenes/multiple_players_tracker.gd

@@ -42,6 +42,7 @@ func find_name(player_name: String) -> SinglePlayerTracker:
 			return tracker
 	return null
 
+
 ## Create a new [SinglePlayerTracker] for the given peer id, or return the one that already exists.
 @rpc("authority", "call_local", "reliable")
 func create(peer_id: int) -> SinglePlayerTracker:

scenes/single_peer_tracker.gd

@@ -0,0 +1,12 @@
+extends Node
+class_name SinglePeerTracker
+
+## Node representative of a single connected peer.
+## 
+## That specific peer must have authority over this node.
+##
+## Then, that authority is used to connect to a specific player.
+
+@rpc("authority", "call_local", "reliable")
+func takeover(player: SinglePlayerTracker):
+	pass

scenes/single_peer_tracker.tscn

@@ -0,0 +1,6 @@
+[gd_scene load_steps=2 format=3 uid="uid://gabtrafmbrmn"]
+
+[ext_resource type="Script" path="res://scenes/single_peer_tracker.gd" id="1_pofmw"]
+
+[node name="SinglePeerTracker" type="Node"]
+script = ExtResource("1_pofmw")

scenes/single_player_tracker.gd

@@ -1,4 +1,4 @@
-extends MultiplayerSynchronizer
+extends Node
 class_name SinglePlayerTracker
 
 ## Node representative of a player connected to the room.
@@ -13,3 +13,25 @@ var player_color: Color = Color.WHITE
 
 ## Whether this player is currently connected or not.
 var player_connected: bool = false
+
+## Change the name of this player.
+@rpc("authority", "call_local", "reliable")
+func set_player_name(value: String):
+	player_name = value
+
+## Change the color of this player.
+@rpc("authority", "call_local", "reliable")
+func set_player_color(value: Color):
+	player_color = value
+
+## Ask the authority for this player to repeat the player's name.
+@rpc("any_peer", "call_local", "reliable")
+func query_player_name():
+	if is_multiplayer_authority():
+		set_player_name.rpc(player_name)
+
+## Ask the authority for this player to repeat the player's color.
+@rpc("any_peer", "call_local", "reliable")
+func query_player_color():
+	if is_multiplayer_authority():
+		set_player_color.rpc(player_color)

scenes/single_player_tracker.tscn

@@ -1,25 +1,6 @@
-[gd_scene load_steps=3 format=3 uid="uid://drccgvtcng3ju"]
+[gd_scene load_steps=2 format=3 uid="uid://drccgvtcng3ju"]
 
 [ext_resource type="Script" path="res://scenes/single_player_tracker.gd" id="1_jwlkv"]
 
-[sub_resource type="SceneReplicationConfig" id="SceneReplicationConfig_755wr"]
+[node name="SinglePlayerTracker" type="Node"]
-properties/0/path = NodePath(".:player_connected")
-properties/0/spawn = true
-properties/0/replication_mode = 2
-properties/1/path = NodePath(".:player_name")
-properties/1/spawn = true
-properties/1/replication_mode = 2
-properties/2/path = NodePath(".:player_color")
-properties/2/spawn = true
-properties/2/replication_mode = 2
-properties/3/path = NodePath(".:strokes_per_hole")
-properties/3/spawn = true
-properties/3/replication_mode = 2
-
-[node name="SinglePlayerTracker" type="MultiplayerSynchronizer"]
-root_path = NodePath(".")
-replication_interval = 1.0
-delta_interval = 0.125
-replication_config = SubResource("SceneReplicationConfig_755wr")
-visibility_update_mode = 2
 script = ExtResource("1_jwlkv")