Stealth addresses represent an approach to enhancing privacy within public and distributed blockchains, such as Ethereum and Bitcoin. Stealth address protocols employ a distinct, randomly generated address for the recipient, thereby concealing interactions between entities. In this study, we introduce BaseSAP, an autonomous base-layer protocol for embedding stealth addresses within the application layer of programmable blockchains. BaseSAP expands upon previous research to develop a modular protocol for executing unlinkable transactions on public blockchains. BaseSAP allows for the development of additional stealth address layers using different cryptographic algorithms on top of the primary implementation, capitalizing on its modularity. To demonstrate the effectiveness of our proposed protocol, we present simulations of an advanced Secp256k1-based dual-key stealth address protocol. This protocol is developed on top of BaseSAP and deployed on the Ethereum test network as the first prototype implementation. Furthermore, we provide cost analyses and underscore potential security ramifications and attack vectors that could affect the privacy of stealth addresses. Our study highlights the flexibility of the BaseSAP protocol and provides insights into the broader implications of stealth address technology in the realm of blockchain privacy.