Hello,
The reason your rules did not work is because you are linking two different rules to the same event. To better explain this, when rule 600001 is triggered with the anchor event ID 4672, and you link rule 600002 to rule 600001, and you make the anchor event ID 4688. Every time rule 600001, which is the parent, is triggered, the event ID will always be 4672, and since you have link 600002 to it, it will never fire because the event will always be 4672, and 4688 will never match.
I see what you are trying to do in terms of correlation, but please also note that these two events are not necessarily going to be linked because event ID 4688 is process execution. But if you intend to link them, you need a third rule, and the two rules for admin logon and process execution have to be independent. Please refer to the sample below for your reference.
<group name="windows,admin_execution">
<!-- Admin logon -->
<rule id="100001" level="3">
<field name="win.system.eventID">4672</field>
<description>Admin privileges assigned to $(win.eventdata.subjectUserName)</description>
</rule>
<!-- Process executed AFTER admin privileges -->
<rule id="100002" level="12">
<field name="win.system.eventID">4688</field>
<description>ADMIN EXECUTION:User: $(win.eventdata.subjectUserName)Process: $(win.eventdata.newProcessName)CommandLine: $(win.eventdata.commandLine)</description>
<mitre>
<id>T1059</id>
</mitre>
</rule>
</group>
<group name="testing,">
<rule id="100003" level="12" timeframe="360">
<if_matched_sid>100001</if_matched_sid>
<if_sid>100002</if_sid>
<description>rule 100003 triggers after rule 100001 and 100002 triggered</description>
</rule>
</group>
Rule 100003 triggers after the execution of rules 100001 and 100002. This is to assume the admin logs in and executes a process and not vice versa.
One point to note when creating custom rules is to always use ID numbers between 100000 and 120000 for custom rules to avoid conflicts with out-of-the-box system rules. I have updated this in the rule I shared above.
Please let me know if you need further assistance on this.