I'm pretty sure Chip and Fast RAM access on an Amiga 1000 does not support FPM access.
Which Amiga system, chipset or motherboard "glue logic" first introduced FPM access to Fast RAM? Which one to Chip RAM?
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Page mode, and later fast page mode (FPM) and static column DRAM only became popular about 1990. Amazingly, the Amiga A3000, also released in 1990, supported faster access to FAST RAM using static column DRAM. The "Ramsey" custom chip was primarily responsible, and versions of "Ramsey" were also used in the A4000. This was only really useful when combined with the new "burst mode" of the 68030 CPU in the A3000. Burst mode allowed the '030 to read 16-bytes (4x32 bit) into its cache using the lower latency of static column and page mode.
Without at least a 68030 CPU, there was no burst mode on an Amiga and limited ability to use this DRAM feature to improve performance. The only Amigas to ship with a 68030 (or 68040) CPU were the A2500/030, A3000, and A4000. But the A2630 accelerator used in the A2500/030 did not support burst mode and wouldn't benefit much from the enhanced DRAM. This leaves only the A3000 and A4000 supporting it.
For CHIP RAM access, improvements were made to the bandwidth for the A3000 by supporting 32-bit access to the CHIP RAM by the CPU. However, there was no burst mode supported for accessing CHIP RAM. For custom chips, the A3000 used ECS, which only allowed 16-bit access without page mode.
With the advent of AGA in the A4000 and A1200 (and later CD32), both the custom chips and CPU could reach CHIP RAM using 32-bit accesses, plus at higher clock speeds. This greatly improved CHIP RAM bandwidth without relying on page mode, and I don't think page mode was supported by the AGA chip set. This leaves only the A4000 with the possibility of CPU access to both FAST RAM and CHIP RAM using page mode.