The scenario you describe, where one Siamese twin observes the double-slit experiment and the other does not, presents an interesting thought experiment regarding the implications of quantum mechanics and entanglement. However, it is important to note that Siamese twins are physically conjoined siblings and not necessarily connected at the level of brain structures, as each twin typically has their own individual brain.
Assuming that the twins do share a brain structure, and that quantum mechanics operates on the level of their shared consciousness, the outcome of the double-slit experiment would depend on the interpretation of quantum mechanics you adopt.
In the Copenhagen interpretation, which is one of the widely accepted interpretations, the act of measurement collapses the quantum state into a definite outcome. If one twin observes the double-slit experiment, their act of observation would collapse the quantum state of the system. As a result, the interference pattern or the particle-like behavior would be determined by that measurement.
On the other hand, if you consider the many-worlds interpretation, it suggests that the universe splits into multiple branches or parallel realities with every possible outcome. In this case, both possibilities—interference pattern and particle-like behavior—would occur in different branches, and each twin would experience a different outcome in their respective realities.
It's important to note that the scenarios I described are purely speculative, as we do not have empirical evidence or a scientific basis for a shared consciousness or quantum effects at the level of brain structures in Siamese twins. Quantum mechanics operates at the microscopic level, and its application to macroscopic systems, such as the human brain, is still a topic of ongoing research and debate.