The best way to implement this feature is to use an Account custom trigger. A trigger is a piece of Apex code that executes before or after a record is inserted, updated, deleted, or undeleted1. In this case, the trigger should execute before an Account record is updated and check if the Postal Code field has changed. If so, the trigger should query the postalCodeToTimezone_c custom object to find the matching Timezone value and assign it to the custom Account text field named Timezone. This way, the Timezone field will be updated automatically based on the Postal Code field.
An Account approval process is not suitable for this feature, as it is used to automate the process of approving records based on predefined criteria and actions2. An Account assignment rule is also not suitable, as it is used to assign ownership of Account records to users or queues based on criteria3. An Account workflow rule is not suitable either, as it is used to automate tasks, email alerts, field updates, and outbound messages based on criteria and evaluation rules4. None of these options can update the Timezone field based on the values in a custom object.
References:
* Apex Developer Guide - Triggers
* Salesforce Help - Approval Processes
* Salesforce Help - Assignment Rules
* Salesforce Help - Workflow Rules