I'm not sure you need to call your timer routine in each worksheet. You really only need one routine and knowledge of which worksheet to assign the times to.
One way would be with a kind of control panel of buttons on a UserForm
. It might look something like this (just 3 worksheets as example):

Then you'd handle all of the click events within the UserForm
code. In this example, I've created a collection of Worksheets and each item is accessed by a string key which is the button's name. Skeleton code would be:
Option Explicit
Private Const START_COLOUR As Long = &HFF00&
Private Const START_TEXT As String = "Start"
Private Const STOP_COLOUR As Long = &HFF&
Private Const STOP_TEXT As String = "Stop"
Private mSheets As Collection
Private Sub btnClock1_Click()
StartStopButton btnClock1
End Sub
Private Sub btnClock2_Click()
StartStopButton btnClock2
End Sub
Private Sub btnClock3_Click()
StartStopButton btnClock3
End Sub
Private Sub StartStopButton(btn As CommandButton, Optional initialise As Variant)
Dim ws As Worksheet
Dim v As Variant
Dim startTime As Date
Set ws = mSheets(btn.Name)
ws.Activate
If Not IsMissing(initialise) Then
'Initialise the button and sheet
SetProperties btn, CBool(initialise)
ws.Range("A1").Value = "Not yet actioned"
ws.Range("B1:D1").ClearContents
Else
If btn.BackColor = START_COLOUR Then
'Set clock running
SetProperties btn, True
ws.Range("A1").Value = "Running"
ws.Range("B1").Value = Now
ws.Range("C1:D1").ClearContents
Else
'Stop clock and calculate difference
SetProperties btn, False
ws.Range("A1").Value = "Stopped"
ws.Range("C1").Value = Now
v = ws.Range("B1").Value
If Not IsEmpty(v) And IsDate(v) Then
'For DateDiff, choose whichever unit you want, I've used seconds ("s")
ws.Range("D1").Value = DateDiff("s", v, Now)
End If
End If
End If
End Sub
Private Sub SetProperties(btn As CommandButton, running As Boolean)
With btn
If running Then
.Caption = STOP_TEXT
.BackColor = STOP_COLOUR
Else
.Caption = START_TEXT
.BackColor = START_COLOUR
End If
End With
End Sub
Private Sub UserForm_Initialize()
Dim ws As Worksheet
'Assign all worksheets to collection
Set mSheets = New Collection
Set ws = ThisWorkbook.Worksheets("Sheet1")
mSheets.Add ws, btnClock1.Name
Set ws = ThisWorkbook.Worksheets("Sheet2")
mSheets.Add ws, btnClock2.Name
Set ws = ThisWorkbook.Worksheets("Sheet3")
mSheets.Add ws, btnClock3.Name
'Set all buttons to start
StartStopButton btnClock1, False
StartStopButton btnClock2, False
StartStopButton btnClock3, False
End Sub