Here is a list of eycleshymer's I have found. Unfortunately, they have deceased. But, still helpful!
ALBERT EYCLESHYMER Request Information
SSN 324-03-8192 Residence: 49801 Iron Mountain, Dickinson, MI
Born 20 Jan 1902 Last Benefit:
Died May 1982 Issued: IL (Before 1951)
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ANDREW EYCLESHYMER Request Information
SSN 026-52-9735 Residence: 01862 North Billerica, Middlesex, MA
Born 3 Apr 1971 Last Benefit:
Died 8 Aug 1996 Issued: 026 (1974 And 1975)
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ANNIE EYCLESHYMER Request Information
SSN 013-26-4138 Residence: 02164 Newton, Middlesex, MA
Born 7 Aug 1872 Last Benefit:
Died Jan 1973 Issued: 013 (Before 1951)
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BERTHA EYCLESHYMER Request Information
SSN 124-18-0526 Residence: 12303 Schenectady, Schenectady, NY
Born 20 Jun 1896 Last Benefit:
Died Jul 1974 Issued: NY (Before 1951)
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DOROTHY EYCLESHYMER Request Information
SSN 105-42-6630 Residence: 13032 Canastota, Madison, NY
Born 4 Jan 1905 Last Benefit:
Died May 1985 Issued: NY (1967)
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FLORENCE EYCLESHYMER Request Information
SSN 065-38-7008 Residence:
Born 5 Aug 1890 Last Benefit:
Died Jan 1989 Issued: 065 (1963)
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GEORGE EYCLESHYMER Request Information
SSN 032-20-5411 Residence: 01778 Wayland, Middlesex, MA
Born 18 Sep 1928 Last Benefit:
Died 6 May 1994 Issued: 032 (Before 1951)
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GEORGE EYCLESHYMER Request Information
SSN 012-03-0812 Residence: 01778 Wayland, Middlesex, MA
Born 31 Oct 1900 Last Benefit:
Died 15 Nov 1993 Issued: 012 (Before 1951)
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GERTRUDE EYCLESHYMER Request Information
SSN 313-10-4292 Residence: 49120 Niles, Berrien, MI
Born 14 May 1911 Last Benefit:
Died 30 Jun 1996 Issued: IN (Before 1951)
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H EYCLESHYMER Request Information
SSN 029-05-1434 Residence: 99362 Walla Walla, Walla Walla, WA
Born 10 Mar 1911 Last Benefit:
Died May 1978 Issued: 029 (Before 1951)