Updates
Some updates from our discussion in comments:
If you don't know the installation URL, you can obtain the 04t key by running:
force:package:installed:list on the scratch org. In Eric's case, adding the package key to his sfdx-project.json still resulting in a failure during package building.
For reference, here's the whole sfdx-project.json from a 2GP package of mine that depends on managed 1GP packages:
{ "packageDirectories": [ { "path": "force-app", "package": "My Package", "versionName": "ver 0.6", "versionNumber": "0.6.0.NEXT", "default": true, "dependencies": [ { "subscriberPackageVersionId": "04t1..." }, { "subscriberPackageVersionId": "04t5..." } ], "ancestorVersion": "0.5.0.1" } ], "namespace": "nebc", "sfdcLoginUrl": "https://login.salesforce.com", "sourceApiVersion": "43.0", "packageAliases": { "My Package": "0Ho...", "My [email protected]": "04t...rQAC", "My [email protected]": "04t...1QAC", "My [email protected]": "04t...6QAC", "My [email protected]": "04t...QQAS", "My [email protected]": "04t...VQAS", "My [email protected]": "04t...bQAC" } }