In addition to the glass ink box RD 75988, registered by Eliezer Edwards, Birmingham on 15 January 1851 - Parcel, I have so far found another five of his glass design registrations so far by searching TNA online design registration summaries:
RD 109830, registered 30 April 1857- Parcel 4. Subject: Flower trainer or support. Class 3: glass
RD 155257, registered 1 October 1862 - Parcel 3. Description: Inkstand. Class 3: glass.
RD 164138, registered 9 July 1863 - Parcel 8. Subject: Inkstand. Class 3: glass
RD 197154, registered May 8 1866 - Parcel 2 (with registrant's address given as 49 St. Paul's Square, Birmingham). No description of item given. Class 3 : glass.
RD 221520, registered 12 September 1868 - Parcel 2 (with registrant given as E Edwards, with address as 49 St. Paul's Square, Birmingham). No description of item given. Class 3: glass.
St Paul’s Square, is a Georgian square in the Jewellery Quarter of Birmingham, and named after the church which still stands in its centre. It is the last remaining Georgian square in the city. Built 1777–79 on the Newhall estate of the Colmore family, it was an elegant and desirable location in the mid-nineteenth century. At the end of the nineteenth century the square was swallowed by workshops and factories, with the fronts of some buildings being pulled down to make shop fronts or factory entrances. Much restoration was done in the 1970s and many of the buildings are Grade II listed.
No. 49 no longer seems to exist in its mid-Victorian form, but it seems unlikely that the address would have been a factory or manufacturing base at that time. I've done a few quick Birmingham directory and genealogy searches but, unfortunately, I haven't been able to find Eliezer Edwards so far.
TNA also has the following (non-glass) design registration records with Eliezer Edwards as registrant:
RD 72305, registered 3 October 1850. Description: Tray for Inkstand. Class 1: metal.
Useful Registered Design Number: 2973, registered 7 October 1851. Subject: Inkstand. Category: Drawing, Geometrical and Mathematical Instruments, Pen, Holder, Pencil, Writing Materials, Inkstands, Desks, Colours and Sketch Boxes.
Useful Registered Design Number: 3826 registered April 10 1856. Subject: Insect trap. Category: Traps for Birds, Vermin, Insects. (Class I, Metal). Remarks: 699 provisional registration.
RD 136881, registered 21 December 1860. Subject: Cover for an inkstand. Class 1: metal.
RD 157526, registered 17 November 1862. Description: Perforated Metallic Box. Class 1: metal.
Provisional registered design number 626, registered 22 November 1862. Subject: Perforated metallic box.
Provisional registered design number 627, registered 22 November 1862. Subject: Perforated metallic box.
Provisional registered design number 628, registered 22 November 1862. Subject: Perforated metallic box.
RD 158049, registered 3 December 1862. Description: Writing Tablet and Linen Stretcher. Class 1: metal.
RD 191168, registered 20 October 1865. No description of item. Class 1: metal.
RD 191243, registered 23 October 1865. Subject: [Rod bracket ? With bird and tendril detail]. Class 1: metal
RD 197153, registered May 8 1866. Subject: [Posy or buttonhole pin]. Class 4: earthenware
RD 197297, registered May 10 1866. Subject: [Metal ornamental design ?]. Class 1: metal
RD 209857, registered July 30 1867. No description. Class 1: metal.
RD 218325, registered 22 April 1862. Subject: [Buckle]. Class 1: metal
RD 227613, registered 3 March 1869. Description: Steel pen or match box.
From the nature and variety of these registrations I think it is most likely that Eliezer Edwards was a retailer, wholesaler or manufacturer's agent for small ornamental domestic effects or stationery items.
Fred.