As promised, here is the safe restart PowerShell script version that includes writing output to the Event Log.

I used the Write-Eventlog command to get the output into the event log.   I started by defining the variables.   The eventID and eventSource can be anything, eventLog and eventType need to match the parameters of the Write-Eventlog command.

#eventlog vars
 $eventLog = "System"
 $eventType = "Information"
 $eventID = 212
 $eventSource = "SafeRestart"

Next, I checked if the event source exists on the computer and if not, create it.

if (!(Get-Eventlog -LogName $eventLog -Source $eventSource)){
New-EventLog -LogName $eventLog -Source $eventSource
}

Lastly, I added the Write-Eventlog command and variables to the script so it creates a message when one of the actions are ran.  Below is the output of one of he messages.

Write-Eventlog -LogName $eventLog -Source $eventSource -EntryType $eventType -EventID $eventID -Message "Will not reboot, outside of maintenance hours"

Here is the finished version of the script:

#v2 adds writing output to the event log
#eventlog vars
 $eventLog = "System"
 $eventType = "Information"
 $eventID = 212
 $eventSource = "SafeRestart"

#declare the day of the month for a reboot
 [int]$rebootDay = 22

#set the minimum days before reboot
 [int]$rebootAge = 1

#get the current day of the month and hour
 [int]$hour = get-date -format HH
 [int]$day = get-date -format dd

#get the number of days the server has been running. Returns "0" if less than 24 hours
 $os=Get-WmiObject win32_operatingsystem
 $uptime = ((get-date) - ($os.ConvertToDateTime($os.lastbootuptime))).Days

#Create the new event source
if (!(Get-Eventlog -LogName $eventLog -Source $eventSource)){
New-EventLog -LogName $eventLog -Source $eventSource
}

#Run the restart
If($hour -lt 12 -or $hour -gt 16){ Write-Eventlog -LogName $eventLog -Source $eventSource -EntryType $eventType -EventID $eventID -Message "Will not reboot, outside of maintenance hours" }
 ElseIf($day -ne $rebootDay) { Write-Eventlog -LogName $eventLog -Source $eventSource -EntryType $eventType -EventID $eventID -Message "Will not reboot, outside of maintenance day" }
 ElseIf($uptime -lt $rebootAge) { Write-Eventlog -LogName $eventLog -Source $eventSource -EntryType $eventType -EventID $eventID -Message "Will not reboot, rebooted within 24 hours" }
 Else{
 (Write-Eventlog -LogName $eventLog -Source $eventSource -EntryType $eventType -EventID $eventID -Message "This system will be restarted by the SafeRestart Powershell Script")
 (restart-computer -force)
 }

*This script is “as is” with no warranties.  Test it before you trust it!