When Vallejo Police Chief Jack E. Stiltz questioned whether the author of the trinity of letters on July 31st 1969 was the same person as the killer, Zodiac's response was immediate in the 'Debut of Zodiac' letter the following morning, supplying more details of the first two crimes at Lake Herman Road and Blue Rock Springs to the police chief.
To prove his link to the murder of Paul Stine, he brought the crime scene to his correspondence by mailing a section of Paul Stine's blooded shirt to the San Francisco Chronicle on October 13th 1969 and November 9th 1969. The Zodiac did the reverse at Lake Berryessa two weeks earlier, taking his writing to the crime scene, and detailing his previous crimes in marker pen on the car door of Bryan Hartnell's 1956 white Karmann Ghia. The Zodiac Killer clearly took risks in every crime he committed, in particular, placing two phone calls after the Blue Rock Springs Park and Lake Berryessa attacks, wandering around Lake Berryessa in an executioner's outfit and tearing a section of blooded shirt from the dead taxicab driver in the heart of San Francisco, to name but a few. Many people have questioned his involvement in each of the crimes and the Zodiac Killer obliged every time, either by providing details only he and the police knew, placing his handwriting at Berryessa, or mailing a swatch of Paul Stine's shirt to the newspapers. For some people, there is nothing the Zodiac could have done to prove the letters and murders were linked. But he didn't have to claim any of the crimes after the Lake Herman Road murders to prove he was the killer. The answer lies in the words of Chief of Police Martin Lee who said "ballistics had confirmed a different weapon was used in three of the attacks."
All Zodiac had to do was use the same weapon at Lake Herman Road, Blue Rock Springs and Presidio Heights, and ballistics and shell casing analysis would have confirmed that the three attacks were inextricably linked, or at the very least left little doubt. He could have taken something from the previous crime scene and deposited it at the following. This would have saved the Zodiac Killer the effort of proving he was the killer in all four attacks. Yet the Zodiac Killer changed his weapon every time, casting doubt on all the crimes being linked. This left the Zodiac having to ultimately prove his association with each crime via his correspondence.
So what can we take from this? Zodiac was prepared to take risks, but was not prepared to extend this risk for weeks or months between his crimes, despite the fact that hiding the weapon away from his home residence would seem to be foolproof if the gun was not registered or had not possessed any identifying features.
The overarching belief is that the Zodiac Killer disposed of each weapon immediately after each crime. The quicker you can separate yourself from the 'smoking gun' the better. But we still have the conflict of a killer quite prepared to take innumerable risks in the commission of his crimes, but wastes not a second in the disposing a weapon he could easily conceal.
In all probability, even if the Zodiac Killer had used the same weapon at Lake Herman Road, Blue Rock Springs Park, Presidio Heights, and had also shot both Cecelia Shepard and Bryan Hartnell at Lake Berryessa with the same gun, you can guarantee that some internet sleuths would still find a way to circumnavigate the evidence and cast doubt on one or more of these crimes once again.