Two actions that would successfully write send time variables to their Send Log are:
Match an AMPscript variable name to a Send Log field. This action will allow the customer to write the value of an AMPscript variable to a corresponding field in the Send Log data extension. For example, if the customer has a Send Log field named ProductName and an AMPscript variable named @ProductName, then the value of @ProductName will be written to the ProductName field in the Send Log.
Use the WriteToLog() AMPscript function in the content. This action will allow the customer to write one or more values to a specified field in the Send Log data extension using an AMPscript function. For example, if the customer wants to write the value of @ProductName and @ProductPrice to the ProductInfo field in the Send Log, they can use WriteToLog("ProductInfo",@ProductName,@ProductPrice) in their content.
Ensuring the send log is linked in an attribute group is not necessary for writing send time variables to their Send Log, as it is only used for creating relationships between data sources in Contact Builder. Enabling send logging to a data extension during send process is not an action that would write send time variables to their Send Log, as it is only a setting that enables or disables send logging for a specific email send. Reference: https://help.salesforce.com/s/articleView?id=sf.mc_es_create_a_sendlog_data_extension.htm&type=5 https://help.salesforce.com/s/articleView?id=sf.mc_es_write_to_the_send_log.htm&type=5