help with VBA conditional notification emails

We really just want to check if the send_mail sub is being called, right? You claim that the send_mail sub is not being called. To check this, we write the simplest code. If there is data in column J, it means that the send_mail sub is being called.

Public k As Long
...
Sub send_mail()
    k = k + 1
    Worksheets("Schedule").Range("J" & k).Value = Format(Now, "yyyy.mm.dd hh:mm")
    
    UpdateClock
End Sub

I will provide the file again, but you must ensure:

1. The file contains only 1 sheet Schedule and my code, without your sheets and codes. Because we will only check my code, right? We do not know what your code does, and whether it does not affect my code. And we only want to check my code.

2. You cannot change, add, delete anything.

3. Download the attached file --> run the file --> leave it for a few hours --> see if there is data in column J entered by sub send_mail.

code in ThisWorkbook

Private Sub Workbook_BeforeClose(Cancel As Boolean)
On Error Resume Next
    Application.OnTime lastTime, "send_mail", , False
End Sub

Private Sub Workbook_Open()
    UpdateClock
End Sub

code in Module1

Option Explicit

Public lastTime As Double
Public k As Long

Private Function readTime()
Dim day As Long, lastRow As Long, i As Long, curr_time As Double
    curr_time = 0
    day = Weekday(Date)
    With Worksheets("Schedule")
        lastRow = .Cells(Rows.Count, day).End(xlUp).Row
        For i = 2 To lastRow
            If .Cells(i, day).Value > Time Then
                curr_time = .Cells(i, day).Value
                Exit For
            End If
        Next i
        If curr_time = 0 Then curr_time = Date + 1 + .Cells(2, (day Mod 7) + 1).Value     
    End With
    readTime = curr_time
End Function

Sub UpdateClock()
Dim curr_time As Double
    curr_time = readTime
    If curr_time = 0 Then
        Application.OnTime lastTime, "send_mail", , False
    Else
        lastTime = curr_time
        Application.OnTime lastTime, "send_mail"
    End If
End Sub

Sub send_mail()
    k = k + 1
    Worksheets("Schedule").Range("J" & k).Value = Format(Now, "yyyy.mm.dd hh:mm")
    
    UpdateClock
End Sub

I added in function readTime

If curr_time = 0 Then curr_time = Date + 1 + .Cells(2, (day Mod 7) + 1).Value

In the previous readTime the code reaches the last hour and turns off the clock. With the above line the code reaches the last hour then takes the first hour of the next day.